Polyrate 17-C Manual · 2021. 7. 17. · Polyrate 2 Executive summary: Polyrate 17-C is a suite of...
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Polyrate 1 Polyrate 17-C Manual Jingjing Zheng, Junwei Lucas Bao, Rubén Meana-Pañeda, Shuxia Zhang, Benjamin J. Lynch, José C. Corchado, Yao-Yuan Chuang, Patton L. Fast, Wei-Ping Hu, Yi-Ping Liu, Gillian C. Lynch, Kiet A. Nguyen, Charles F. Jackels, Antonio Fernandez Ramos, Benjamin A. Ellingson, Vasilios S. Melissas, Jordi Villà , Ivan Rossi, Elena. L. Coitiño, Jingzhi Pu, Titus V. Albu Department of Chemistry, Chemical Theory Center, and Minnesota Supercomputing Institute, University of Minnesota, Minneapolis, Minnesota 55455 Artur Ratkiewicz Institute of Chemistry, University of Bialystok, Poland Rozeanne Steckler Northwest Alliance for Computational Science & Engineering, Oregon State University, Corvallis, Oregon 97331 Bruce C. Garrett Environmental Molecular Sciences Laboratory, Pacific Northwest National Laboratory, Richland, Washington 99352 Alan D. Isaacson Department of Chemistry and Biochemistry,Miami University, Oxford, Ohio 45056 and Donald G. Truhlar Department of Chemistry, Chemical Theory Center, and Minnesota Supercomputing Institute, University of Minnesota, Minneapolis, Minnesota 55455 Most recent changes to program: June 16, 2018 for the part excluding the SS-QRRK utility; Dec. 22, 2018 for SS-QRRK utility. Most recent update to manual: July 17, 2021 Polyrate 17-C is available from the Truhlar Research Group Software site at https://comp.chem.umn.edu/polyrate/ Polyrate 17-C is being submitted to the Computer Physics Communications Program Library, and after acceptance it will also be available from the CPC Program Library at https://data.mendeley.com/journal/00104655? The code is made available free of charge. Licensing: The Polyrate 17-C code is licensed under the Apache-2.0 license. The Polyrate 17-C manual is licensed under the CC-BY-4.0 license.
Transcript of Polyrate 17-C Manual · 2021. 7. 17. · Polyrate 2 Executive summary: Polyrate 17-C is a suite of...
Polyrate 1
Polyrate 17-C Manual
Jingjing Zheng, Junwei Lucas Bao, Rubén Meana-Pañeda, Shuxia Zhang,
Benjamin J. Lynch, José C. Corchado, Yao-Yuan Chuang, Patton L. Fast, Wei-Ping Hu, Yi-Ping Liu, Gillian C. Lynch, Kiet A. Nguyen, Charles F. Jackels,
Antonio Fernandez Ramos, Benjamin A. Ellingson, Vasilios S. Melissas, Jordi Villà, Ivan Rossi, Elena. L. Coitiño, Jingzhi Pu, Titus V. Albu
Department of Chemistry, Chemical Theory Center, and Minnesota Supercomputing Institute, University of Minnesota, Minneapolis, Minnesota 55455
Artur Ratkiewicz
Institute of Chemistry, University of Bialystok, Poland
Rozeanne Steckler
Northwest Alliance for Computational Science & Engineering,
Oregon State University, Corvallis, Oregon 97331
Bruce C. Garrett
Environmental Molecular Sciences Laboratory,
Pacific Northwest National Laboratory, Richland, Washington 99352
Alan D. Isaacson
Department of Chemistry and Biochemistry,Miami University, Oxford, Ohio 45056
and Donald G. Truhlar
Department of Chemistry, Chemical Theory Center, and Minnesota Supercomputing Institute, University of Minnesota, Minneapolis, Minnesota 55455
Most recent changes to program:
June 16, 2018 for the part excluding the SS-QRRK utility;
Dec. 22, 2018 for SS-QRRK utility.
Most recent update to manual: July 17, 2021
Polyrate 17-C is available from the Truhlar Research Group Software site at
https://comp.chem.umn.edu/polyrate/
Polyrate 17-C is being submitted to the Computer Physics Communications Program
Library, and after acceptance it will also be available from the CPC Program Library at
https://data.mendeley.com/journal/00104655?
The code is made available free of charge.
Licensing:
The Polyrate 17-C code is licensed under the Apache-2.0 license.
The Polyrate 17-C manual is licensed under the CC-BY-4.0 license.
Polyrate 2
Executive summary:
Polyrate 17-C is a suite of computer programs for the calculation of chemical
reaction rates of polyatomic species (including atoms and diatoms as special cases) by
variational transition state theory (VTST); conventional transition state theory is also
supported. Polyrate 17-C (called Polyrate for short) consists of the main program,
called Polyrate, and a set of utility codes,
Polyrate can calculate the rate constants for both bimolecular reactions and
unimolecular reactions, and it can be applied to reactions in the gas-phase, liquid-solution
phase, or solid-state and to gas-solid-interface reactions. Polyrate can perform variational
transition state theory (VTST) calculations on gas-phase reactions with both tight and
loose transition states. For tight transition states it uses the reaction-path (RP)
variational transition state theory developed by Garrett and Truhlar, and for loose
transition states it uses variable-reaction-coordinate (VRC) variational transition state
theory developed by Georgievskii and Klippenstein.
The RP methods used for tight transition states are conventional transition state
theory, canonical variational transition state theory (CVT), and microcanonical
variational transition state theory ( VT) with multidimensional semiclassical
approximations for tunneling and nonclassical reflection. The tunneling approximations
available are zero-curvature tunneling (ZCT), small-curvature tunneling (SSCT), large-
curvature- tunneling (LCT), and optimized multidimensional tunneling (OMT). The SCT
option is the centrifugal dominant semiclassical adiabatic ground-state tunneling, and the
LCT options include both LC3 and LC4 including tunneling into excited states. One may
also treat specific vibrational states of selected modes with translational, rotational, and
other vibrational modes treated thermally.
For RP calculations, several options are available for reaction paths, vibrations
transverse to the reaction path, and transition state dividing surfaces. Generalized-
transition-state dividing surfaces may be defined on the basis of gradient directions in
isoinertial coordinates or by the re-orientation of the dividing surface algorithm. Reaction
paths may be calculated by the Euler steepest-descent, Euler stabilization, Page-McIver,
or variational-reaction-path algorithms. Vibrations away from the reaction path may be
defined by rectilinear (not recommended), nonredundant curvilinear, or redundant
curvilinear coordinates. Vibrational frequencies may be unscaled (not recommended) or
scaled.
For VRC calculations, rate constants may be calculated for canonical or
microcanonical ensembles or energy-and-total-angular-momentum resolved
microcanonical ensembles. VRC calculations are most appropriate for barrierless
association reactions. Both single-faceted and multifaceted dividing surfaces are
supported.
Pressure-dependent rate constants for elementary reactions can be computed using
system-specific quantum RRK theory (SS-QRRK) with the information obtained from
high-pressure-limit VTST calculation as input by using the SS-QRRK utility code. The
SS-QRRK utility program is part of the Polyrate distribution, and its usage is described in
a separate manual.
Polyrate 3
Potential energy surfaces may be analytic functions evaluated by subroutines, or
they may be implicit surfaces defined by electronic structure input files or interface
subroutines containing energies, gradients, and force constants (Hessians). The use of
electronic structure calculations to calculate rate constants or other dynamical quantities
without an analytic potential energy surface is called direct dynamics.
Analytic surfaces may be used for variational transition state theory and any of the
types of tunneling calculations, single-level and dual-level calculations based solely on
electronic structure input files may be used for variational transition state theory and
zero-curvature or small-curvature tunneling, and dual-level calculations based on using
an analytic potential energy surface as the lower level and using an electronic structure
input file as the higher level may be used for variational transition state theory and any of
the types of tunneling calculations.
Polyrate supports six options for direct dynamics, namely (i) straight single-level
direct dynamics, (ii) zero-order interpolated variational transition state theory (IVTST-0),
(iii) first-order interpolated variational transition state theory (IVTST-1), (iv) interpolated
variational transition state theory by mapping (IVTST-M), (v) variational transition state
theory with interpolated single-point energies (VTST-ISPE), and (vi) variational
transition state theory with interpolated optimized corrections (VTST-IOC). VTST-IOC
and VTST-ISPE are examples of dual-level direct dynamics; and VTST-IOC is also
called triple-slash dynamics (///), where the triple slash denotes higher-order corrections
of the geometries at which energetic and Hessian corrections are calculated. Dual-level
methods may be applied with electronic structure data for both levels (dual-level direct
dynamics), or it may be applied with an analytical potential energy surface for the lower
level and electronic structure data for the higher level. When dual-level methods are
employed with electronic structure data for both levels, the lower level may be either
straight direct dynamics or IVTST-M.
This version of Polyrate contains 112 test runs, and 46 of these are for direct
dynamics calculations; 85 of the test runs are single-level runs, and 27 are dual-level
calculations.
Polyrate is designed to be used in conjunction with interfaces to electronic
structure programs for direct dynamics. Currently the following interfaces are available
(note that some of the interfaces were created with older versions of Polyrate, but they
should work with Polyrate as well):
Electronic structure package Interface
CHARMM with CHARMMRATE CRATE
GAMESS (or with GAMESSPLUS) GAMESSPLUSRATE
GAUSSIAN 16/GAUSSIAN 09 GAUSSRATE
JAGUAR JAGUARATE
MC-TINKER MC-TINKERATE
MORATE MOPAC
MULTILEVEL MULTILEVELRATE
NWCHEM NWCHEMRATE
Polyrate 4
CONTENTS
TITLE PAGE AND EXECUTIVE SUMMARY ................................................................1
CONTENTS ......................................................................................................................... 4
PART I GENERAL INFORMATION ................................................................................ 12
1. INTRODUCTION..........................................................................................................12
2. RECOMMENDED CITATION FOR POLYRATE 17-C ..............................................................23
3. RECOMMENDED CITATIONS FOR INCORPORATED CODE ..........................................23
4. LICENSING ...................................................................................................................24
5. PROGRAM AND MANUAL DESCRIPTION .............................................................25
5.A. Code description, portability, and special files ......................................................25
5.B. Description of the manual ......................................................................................25
5.B.1. Referencing conventions .................................................................................26
5.B.2. Key references .................................................................................................27
PART II THEORY BACKGROUND AND CALCULATION DETAILS ON RP-VTST .... 28
6. THEORETICAL BACKGROUND ON RP-VTST .........................................................28
6.A. Basic theory............................................................................................................28
6.B. Vibrations, Rotations, and Translations .................................................................31
6.C. Partition functions ..................................................................................................34
6.D. Tunneling methods .................................................................................................35
6.E. Reactant and product properties .............................................................................37
6.F. Saddle point properties ...........................................................................................39
6.G. Reaction path..........................................................................................................40
6.G.1. SADDLE option ..............................................................................................41
6.G.2. NOSADDLE option ........................................................................................44
6.H. Reaction-path curvature .........................................................................................44
6.I. Transmission coefficients ........................................................................................46
6.J. Reaction rates including tunneling ..........................................................................48
6.K. Imaginary-frequency modes transverse to the reaction path..................................50
6.L. Equilibrium constant calculation ............................................................................51
6.M. Omitting the product..............................................................................................51
6.N. Optimized multidimensional tunneling calculations..............................................52
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6.N.1. COMT method ................................................................................................52
6.N.2. µOMT method.................................................................................................52
6.O. Interpolated VTST and mapped interpolation........................................................52
6.O.1. IVTST-0 and IVTST-1....................................................................................53
6.O.2. Interpolated VTST by mapping (IVTST-M)...................................................54
6.O.3. The mapped interpolation (MI) algorithm with the hooks ..............................56
6.P. Interpolated optimized corrections (VTST-IOC), a form of dual-level VTST.......56
6.Q. Interpolated algorithm for large-curvature tunneling calculations.........................58
7. PROGRAM STRUCTURE ............................................................................................59
7.A. Overview of program flow .....................................................................................59
7.B. Determining the sign of s .......................................................................................65
7.C. Restart options ........................................................................................................66
8. CALCULATIONS USING THE HOOKS .....................................................................68
8.A. Methods for interpolating beyond SLM and SLP with the hooks.............................68
8.B. Zero of energy ........................................................................................................68
8.C. User-Supplied analytic potential energy surface ....................................................69
8.C.1. Interface ...........................................................................................................69
8.C.2. Utility routines.................................................................................................72
8.D. Calculations using an electronic structure program through hooks .......................75
9. CALCULATIONS BASED ON AN ELECTRONIC STRUCTURE INPUT FILE.......81
9.A. Relation of Polyrate input to electronic structure package output.........................83
9.B. Orientation of the molecule at generalized transition states...................................84
9.C. Methods for interpolation of electronic structure data with files fu30 and fu40....85
9.D. Methods for interpolation of electronic structure data with file fu31 ....................87
10. SELECTED DETAILS OF THE CALCULATIONS ..................................................88
10.A. Extrapolation of the reaction-path data beyond the range of the original grid ....88
10.B. Options for anharmonicity....................................................................................90
10.B.1. WKB anharmonicity based on a quadratic-quartic fit ...................................91
10.B.2. WKB anharmonicity based on the true potential ..........................................92
10.B.3. Hindered rotor treatments..............................................................................92
10.C. Alternate method for the calculation of numerical second derivatives ................98
10.D. Reaction-path following methods ........................................................................99
10.E. Interpolation of small-curvature effective reduced mass ...................................101
10.F. Reaction-path curvature calculation ...................................................................101
10.G. Solid-state and gas-solid interface reactions ......................................................102
10.H. VTST-IOC calculation, including ICR, ICL, and ICA schemes........................102
Polyrate 6
10.I. VTST-ISPE calculation .......................................................................................106
10.J. Alternative methods for mapped interpolation ....................................................109
10.K. Quantized-reactant-state tunneling calculation ..................................................110
10.L. Curvilinear generalized normal mode analysis ..................................................110
10.M. IVTST0FREQ option ........................................................................................112
10.N. LCG4 option.......................................................................................................116
10.O. MS-VTST, MP-VTST, FMS-VTST, and FMR-VSTT calculations by using both
the Polyrate and MSTOR programs ...............................................................................118
PART III THEORY BACKGROUND FOR VRC-VTST.................................................. 125
11. THEORETICAL BACKGROUND ON VRC-VTST..................................................125
11.A. Variable reaction coordinate ..........................................................................125
11.B. Multifaceted dividing surface.........................................................................131
11.C. Overview of program flow for VRC-VTST calculation ................................132
11.D. Implementation details of the E, J-resolved microcanonical VRC algorithm 132
PART IV DESCRITION OF INPUT FILES..................................................................... 135
12. DESCRIPTION OF INPUT FOR RP-VTST ...............................................................135
12.A. General description of file fu5 input ..................................................................135
12.A.1. Section descriptions ....................................................................................137
12.A.2. GENERAL section ......................................................................................138
12.A.3. ENERGETICS section ................................................................................148
12.A.4. SECOND section ........................................................................................151
12.A.5. OPTIMIZATION section ............................................................................154
12.A.6. REACT1, REACT2, PROD1, PROD2, WELLR, WELLP, AND START
sections .....................................................................................................................161
12.A.7. PATH section ..............................................................................................181
12.A.8. TUNNEL section.........................................................................................213
12.A.9. RATE section ..............................................................................................224
12.B. General description of file fu29 input ................................................................236
12.B.1. E1GEOM Section ........................................................................................237
12.B.2. E1GRAD Section ........................................................................................237
12.B.3. E1HESS, P1HESS, P2HESS, R1HESS, R2HESS, and TSHESS sections .237
12.B.4. IVTST Section.............................................................................................238
Polyrate 7
12.B.5. P1FREQ, P2FREQ, R1FREQ, R2FREQ, and TSFREQ sections ...............240
12.C. General description of file fu30 input ................................................................241
12.D. General description of file fu31 input ................................................................251
12.D.1. Section descriptions ....................................................................................251
12.D.2 GENERAL section .......................................................................................253
12.D.3. REACT1, REACT2, PROD1, PROD2, WELLR, WELLP, and SADDLE
sections .....................................................................................................................258
12.E. General description of file fu40 input.................................................................261
12.E.1 Section Descriptions .....................................................................................261
12.E.2 GEN40 section..............................................................................................262
12.E.3 R140, R240, P140, P240, WR40, and WP40 sections .................................269
12.E.4 SADDLE40 section ......................................................................................272
12.E.5 POINT40 section ..........................................................................................274
12.F. General description of unit fu50 input ................................................................279
12.G. General description of unit fu51 input ...............................................................291
12.G.1. Section Descriptions....................................................................................291
12.G.2 ISPEGEN section .........................................................................................292
12.G.3 POINT section..............................................................................................296
13. DESCRIPTION OF INPUT FOR VRC-VTST ............................................................298
13.A Section descriptions of input file fu5 ..................................................................298
13.A.1. GENERAL section ......................................................................................298
13.A.2. ENERGETICS section ................................................................................302
13.A.3. OPTIMIZATION section ............................................................................303
13.A.4. REACT1, REACT2, PROD1, AND START sections ................................304
13.A.5. PATH section ..............................................................................................307
13.A.6. RATE section ..............................................................................................308
14. GENERAL DESCRIPTION OF LCT FILES.............................................................309
PART V MORE GENERAL PROGRAM PACKAGE INFORMATION ......................... 310
15. INSTALLING AND USING POLYRATE .....................................................................310
15.A. Instructions for a Unix environment ..................................................................310
15.A.1. Installation ...................................................................................................310
15.A.2. Testing .........................................................................................................316
15.A.3. Using POLYRATE ..........................................................................................318
15.B. Comments for expert users .................................................................................321
Polyrate 8
15.C. Running in parallel using MPI ...........................................................................322
16. SAMPLE TEST RUNS ..............................................................................................325
16.A. Chart of the potential energy functions and data files........................................325
16.B. Descriptions of sample test runs.........................................................................325
16.C.1. Test run ch5j1tr1 .........................................................................................329
16.C.2. Test run ch5j1tr2 .........................................................................................331
16.C.3. Test run ch5j1tr3 .........................................................................................332
16.C.4. Test run ch5j1tr4 .........................................................................................333
16.C.5. Test run ch5j1tr5 .........................................................................................334
16.C.6. Test run ch5j1tr6 .........................................................................................335
16.C.7. Test run ch5j1tr7 .........................................................................................336
16.C.8. Test run ch5j1tr8 .........................................................................................337
16.C.9. Test run ch5j1tr9 .........................................................................................338
16.C.10. Test run ch5j1tr10 .....................................................................................340
16.C.11. Test run ch5j1tr11 .....................................................................................341
16.C.12. Test run ch5j2tr1 .......................................................................................342
16.C.13. Test run ch5j1tr12 .....................................................................................343
16.C.15. Test run ch5j2tr3 .......................................................................................345
16.C.16. Test run ch5j2itr1 ......................................................................................346
16.C.17. Test run ch5j2itr2 ......................................................................................347
16.C.18. Test run ch5fu29tr1 ...................................................................................348
16.C.19. Test run ch5fu29tr2 ...................................................................................349
16.C.20. Test run ch5fu30tr1 ...................................................................................350
16.C.21. Test run ch5fu30tr2 ...................................................................................351
16.C.22. Test run ch5fu30tr3 ...................................................................................352
16.C.23. Test run ch5fu30tr4 ...................................................................................353
16.C.24. Test run ch5fu30tr5 ...................................................................................354
16.C.25. Test run ch5fu30tr6 ...................................................................................355
16.C.26. Test run ch5fu31tr1 ...................................................................................356
16.C.27. Test run ch5fu40tr1 ...................................................................................357
16.C.28. Test run ch5fu40tr2 ...................................................................................358
16.C.29. Test run ch5fu40tr3 ...................................................................................359
16.C.30. Test run ch5fu40tr4 ...................................................................................360
16.C.31. Test run ch5fu40tr5 ...................................................................................361
16.C.32. Test run ch5fu40tr6 ...................................................................................363
16.C.33. Test run ch5fu50tr1 ...................................................................................364
Polyrate 9
16.C.34. Test run ch5fu50tr2 ...................................................................................365
16.C.35. Test run ch5fu50tr3 ...................................................................................366
16.C.36. Test run ch5fu51tr1 ...................................................................................367
16.C.37. Test run ch5icfu30tr1 ................................................................................368
16.C.38. Test run ch5icfu30tr2 ................................................................................369
16.C.39. Test run ch5icfu31tr1 ................................................................................370
16.C.40. Test run ch5icfu40tr1 ................................................................................371
16.C.41. Test run ch5icfu40tr2 ................................................................................372
16.C.42. Test run clhbrtr1 ........................................................................................373
16.C.43. Test run clhbrtr2 ........................................................................................375
16.C.44. Test run clhbrtr3 ........................................................................................376
16.C.45. Test run clhbrtr4 ........................................................................................377
16.C.46. Test run clhbr1tr5 ......................................................................................378
16.C.47. Test run cmctr1..........................................................................................379
16.C.48. Test run cmctr2..........................................................................................380
16.C.49. Test run cmctr3..........................................................................................381
16.C.50. Test run cwmctr1 .......................................................................................382
16.C.51. Test run cwmctr2 .......................................................................................383
16.C.52. Test run cwmctr3 .......................................................................................384
16.C.53. Test run h3tr1 ............................................................................................385
16.C.54. Test run h3tr2 ............................................................................................386
16.C.55. Test run h3tr3 ............................................................................................387
16.C.56. Test run h3tr4 ............................................................................................388
16.C.57. Test run ho2tr1 ..........................................................................................389
16.C.58. Test run ho2tr2 ..........................................................................................390
16.C.59. Test run ho2tr3 ..........................................................................................391
16.C.60. Test run ho2tr4 ..........................................................................................392
16.C.61. Test run ho2tr5 ..........................................................................................393
16.C.62. Test run nh3tr1 ..........................................................................................394
16.C.63. Test run nh3tr2 ..........................................................................................395
16.C.64. Test run oh3tr1 ..........................................................................................396
16.C.65. Test run oh3tr2 ..........................................................................................397
16.C.66. Test run oh3tr3 ..........................................................................................398
16.C.67. Test run oh3tr4 ..........................................................................................399
16.C.68. Test run oh3tr5 ..........................................................................................400
16.C.69. Test run oh3tr6 ..........................................................................................401
Polyrate 10
16.C.70. Test run oh3tr7 ..........................................................................................402
16.C.71. Test run oh3tr8 ..........................................................................................403
16.C.72. Test run oh3tr9 ..........................................................................................404
16.C.73. Test run oh3tr10 ........................................................................................405
16.C.74. Test run oh3fu30tr1 ...................................................................................406
16.C.75. Test run oh3fu30tr2 ...................................................................................407
16.C.76. Test run oh3fu30tr3 ...................................................................................408
16.C.77. Test run oh3fu30tr4 ...................................................................................409
16.C.78. Test run oh3fu30tr5 ...................................................................................410
16.C.79. Test run oh3fu30tr6 ...................................................................................411
16.C.80. Test run oh3fu31tr1 ...................................................................................412
16.C.81. Test run oh3fu31tr2 ...................................................................................413
16.C.82. Test run oh3fu40tr1 ...................................................................................414
16.C.83. Test run oh3fu40tr2 ...................................................................................415
16.C.84. Test run oh3fu40tr3 ...................................................................................416
16.C.85. Test run oh3fu40tr4 ...................................................................................417
16.C.86. Test run oh3fu40tr5 ...................................................................................418
16.C.87. Test run oh3fu40tr6 ...................................................................................419
16.C.88. Test run hnitr1 ...........................................................................................420
16.C.89. Test run h2nitr1 .........................................................................................421
16.C.90. Test run ch4ohtr1.......................................................................................422
16.C.91. Test run ch4ohtr2.......................................................................................423
16.C.92. Test run ch4ohtr3.......................................................................................424
16.C.93. Test run ch4ohtr4.......................................................................................425
16.C.94. Test run ch4cltr1........................................................................................426
16.C.95. Test run ch4cltr2........................................................................................427
16.C.96. Test run ch4otr1.........................................................................................428
16.C.97. Test run ohcltr1 .........................................................................................429
16.C.98. Test run ohcltr2 .........................................................................................430
16.C.99. Test run ohcltr3 .........................................................................................431
16.C.100. Test run ohcltr4 .......................................................................................432
16.C.101. Test run ohcltr5 .......................................................................................433
16.C.102. Test run ch3tr1.........................................................................................434
16.C.103. Test run h3o2fu31tr1 ...............................................................................435
16.C.104. Test run h3o2fu31tr2 ...............................................................................436
16.C.105. Test run h3o2fu31tr3 ...............................................................................437
Polyrate 11
16.C.106. Test run h3o2fu31tr4 ...............................................................................438
16.D. Summary of test runs .........................................................................................439
17. DESCRIPTION OF FILES IN RELEASE OF VERSION 17 ....................................441
17.A. FORTRAN files and subprograms, MODULE files, and PES subroutines ..........441
17.A.1. Polyrate subprograms .................................................................................441
17.A.2 User-supplied subprograms and module files ..............................................488
17.A.3 FORTRAN files ...........................................................................................488
17.B. Utility program detmi.f.......................................................................................491
17.C. Utility program hrotor.f ......................................................................................493
17.D. Utility programs findl.f and findb.f ....................................................................497
17.E. Utility program rotate30.f, rotate31.f, and rotate40.f .........................................497
17.F. Utility program SS-QRRK...................................................................................500
18. UNIX C SHELL SCRIPTS AND PERL SCRIPTS...........................................................501
18.A. Installation script ................................................................................................501
18.B. Potential energy surface compiling scripts.........................................................502
18.C. Source code compiling script .............................................................................503
18.D. Linking script .....................................................................................................504
18.E. Test run scripts....................................................................................................504
19. FILE USAGE .............................................................................................................505
20. CITATIONS INDICATED BY BRACKETS IN THE TEXT....................................508
21. BIBLIOGRAPHY ......................................................................................................512
22. ERRATA ....................................................................................................................523
23. ACKNOWLEDGMENTS..........................................................................................524
24. INDEX .......................................................................................................................525
Polyrate 12
Part I General Information
1. INTRODUCTION
Polyrate 17-C (to be called Polyrate for short) is a suite of programs for the analysis of
reactants, products, and transition states of chemical reactions and for calculating
variational transition state theory (VTST) rate constants and multidimensional
semiclassical tunneling probabilities. The program suite consists of the main program,
called POLYRATE, and a number of utility programs. The program performs two
qualitatively different kinds of VTST calculations:
• RP-VTST: reaction–path VTST for arbitrary kinds of reactions with tight
transition states.
• VRC-VTST: variable-reaction-coordinate VTST only for loose transition states of
bimolecular association reactions or their reverse dissociation reactions.
and it also can calculate pressure-dependent rate constants by using system-specific
quantum Ramsperger–Rice–Kassel theory:
• SS-QRRK: system-specific quantum RRK theory
RP-VTST and VRC-VTST are included in Polyrate proper, and SS-QRRK is performed
in a separate utility code that is included as part of the Polyrate package. The SS-QRRK
utility code is described in a separate manual, which is also included as part of the
Polyrate package.
The following articles contain summaries of the technical background for the
methods in Polyrate:
• "Variational Transition-State Theory," D. G. Truhlar and B. C. Garrett, Accounts
of Chemical Research 13, 440-448 (1980).
doi.org/10.1021/ar50156a00220.
• “Generalized Transition State Theory,” D. G. Truhlar, A. D. Isaacson, and B. C.
Garrett, in Theory of Chemical Reaction Dynamics, edited by M. Baer (CRC
Press, Boca Raton, FL, 1985), Vol. 4, pp. 65–137.
comp.chem.umn.edu/Truhlar/docs/C20.pdf
• “Variational Transition State Theory,” D. G. Truhlar and B. C. Garrett, in Annual
Review of Physical Chemistry, Vol. 35, edited by B. S. Rabinovitch, J. M. Schurr,
and H. L. Strauss (Annual Reviews, Inc., Palo Alto, California, 1984), pp. 159–
189.
doi.org/10.1146/annurev.pc.35.100184.001111
comp.chem.umn.edu/Truhlar/docs/C21.pdf
Polyrate 13
• “POLYRATE: A General Computer Program for Variational Transition State
Theory and Semiclassical Tunneling Calculations of Chemical Reaction Rates,”
A. D. Isaacson, D. G. Truhlar, S. N. Rai, R. Steckler, G. C. Hancock, B. C.
Garrett, and M. J. Redmon, Computer Physics Communications 47, 91-102
(1987).
doi.org/10.1016/0010-4655(87)90069-5
• “Dynamical Formulation of Transition State Theory: Variational Transition States
and Semiclassical Tunneling,” S. C. Tucker and D. G. Truhlar, in New
Theoretical Concepts for Understanding Organic Reactions, edited by J. Bertrán
and I. G. Csizmadia (Kluwer, Dordrecht, The Netherlands, 1989), pp. 291–346.
[NATO ASI Ser. C 267, 291–346 (1989)]
doi.org/10.1007/978-94-009-2313-3_11
comp.chem.umn.edu/Truhlar/docs/UMSI1988-90.pdf
• “POLYRATE 4: A New Version of a Computer Program for the Calculation of
Chemical Reaction Rates for Polyatomics,” D.-h. Lu, T. N. Truong, V. S.
Melissas, G. C. Lynch, Y.-P. Liu, B. C. Garrett, R. Steckler, A. D. Isaacson, S. N.
Rai, G. C. Hancock, J. G. Lauderdale, T. Joseph, and D. G. Truhlar, Computer
Physics Communications 71, 235-262 (1992).
doi.org/10.1016/0010-4655(92)90012-N
• "POLYRATE 6.5: A New Version of Computer Program for the Calculation of
Chemical Reaction Rates for Polyatomics," R. Steckler, W.-P. Hu, Y.-P. Liu, G.
C. Lynch, B. C. Garrett, A. D. Isaacson, V. S. Melissas, D.-h. Lu, T. N. Truong,
S. N. Rai, G. C. Hancock, J. G. Lauderdale, T. Joseph, and D. G. Truhlar,
Computer Physics Communications 88, 341-343 (1995). [new version
announcement] doi.org/10.1016/0010-4655(95)00037-G
• "Transition State Theory," B. C. Garrett and D. G. Truhlar, in Encyclopedia of
Computational Chemistry, edited by P. v. R. Schleyer, N. L. Allinger, T. Clark, J.
Gasteiger, P. A. Kollman, and H. F. Schaefer III (John Wiley & Sons, Chichester,
UK, 1998), Volume 5, pp. 3094-3104.
comp.chem.umn.edu/Truhlar/docs/C58.pdf
• "Variational Transition State Theory and Multidimensional Tunneling for Simple
and Complex Reactions in the Gas Phase, Solids, Liquids, and Enzymes," D. G.
Truhlar, in Isotope Effects in Chemistry and Biology, edited by A. Kohen and H.-
H. Limbach (Marcel Dekker, Inc., New York, 2006), pp. 579-619.
doi.org/10.1201/9781420028027.ch22
• "Variational Transition State Theory in the Treatment of Hydrogen Transfer
Reactions, " D. G. Truhlar and B. C. Garrett, in Hydrogen-Transfer Reactions,
edited by J. T. Hynes, J. P. Klinman, H.-H. Limbach, and R. L. Schowen (Wiley-
VCH, Weinheim, Germany, 2007), Vol. 2, pp. 833-874.
doi.org/10.1002/9783527611546.ch27
comp.chem.umn.edu/Truhlar/docs/C73.pdf
Polyrate 14
• "Variational Transition State Theory," B. C. Garrett and D. G. Truhlar, in Theory
and Applications of Computational Chemistry: The First Forty Years, edited by
C. E. Dykstra, G. Frenking, K. S. Kim, and G. E. Scuseria (Elsevier, Amsterdam,
2005), pp. 67-87. CODEN: 69HSJX
doi.org/10.1016/B978-044451719-7/50048-2
comp.chem.umn.edu/Truhlar/docs/C71.pdf
• "Variational Transition State Theory with Multidimensional Tunneling," A.
Fernandez-Ramos, B. A. Ellingson, B. C. Garrett, and D. G. Truhlar, in Reviews
in Computational Chemistry, Vol. 23, edited by K. B. Lipkowitz and T. R.
Cundari (Wiley-VCH, Hoboken, NJ, 2007), pp. 125-232.
doi.org/10.1002/9780470116449.ch3
comp.chem.umn.edu/Truhlar/docs/C76.pdf
• “Mechanistic Analysis of the Base-Catalyzed HF Elimination from 4-Fluoro-4-
(4'-nitrophenyl)butane-2-one Based on Liquid-Phase Kinetic Isotope Effects
Calculated by Dynamics Modeling with Multidimensional Tunneling,” Y. Kim,
A. V. Marenich, J. Zheng, K. H. Kim, M. Kołodziejska-Huben, M. Rostkowski,
P. Paneth, and D. G. Truhlar, Journal of Chemical Theory and Computation 5, 59-
67 (2009).
doi.org/10.1021/ct800345j
• “Multi-path Variational Transition State Theory for Chemical Reaction Rates of
Complex Polyatomic Species: Ethanol + OH Reactions,” J. Zheng and D. G.
Truhlar, Faraday Discussions 157, 59-88 (2012).
doi.org/10.1039/C2FD20012K.
• “Association of CF2 and Dissociation of C2F4 by Variational Transition State
Theory and System-Specific Quantum RRK Theory,” J. L. Bao, X. Zhang, and D.
G. Truhlar, Proceedings of the National Academy of Sciences U.S.A. 113, 13606-
13611 (2016).
doi.org/10.1073/pnas.1616208113
• “Variational Transition State Theory: Theoretical Framework and Recent
Developments,” J. L. Bao and D. G. Truhlar, Chemical Society Reviews 46,
7548-7596 (2017).
doi.org/10.1039/C7CS00602K
• “Semiclassical Multidimensional Tunneling Calculations,” D. G. Truhlar, in
Tunnelling in Molecules: Nuclear Quantum Effects from Bio to Physical
Chemistry, edited by J. Kaestner and S. Kozuch (RSC Publishing, Cambridge,
2021), pp. 261-282.
doi.org/10.1039/9781839160370-00261
https://truhlar.dl.umn.edu/sites/truhlar.dl.umn.edu/files/c88corrected_proofs.pdf
In Polyrate, analysis of reactants and products can be performed for up to two
reactants and two products for RP-VTST and for two reactants and one product for VRC-
VTST. Polyrate also calculates equilibrium constants and reverse reaction rates, so the
VRC-VTST method can also calculate rate constants for one reactant and two products.
Polyrate 15
The RP-VTST method can be applied to gas-phase, liquid-phase, solid-phase, and gas-
solid-interface reactions; the VRC-VTST method is used for gas-phase reactions.
Generalized transition state theory calculations may be carried out using the
harmonic approximation for vibrations with either rectilinear or curvilinear coordinates in
RP-VTST calculations. It is highly recommended to use curvilinear coordinates (via the
“CURV2” or “CURV3” options) rather than Cartesian coordinates for generalized-
normal mode analysis along the MEP in RP-VTST calculations; Cartesian coordinates
will often yield unphysical imaginary frequencies along the reaction coordinate, and these
will cause unphysical VTST results. One should always check in the long output that the
generalized normal mode frequencies as functions of the reaction coordinate do not
contain any imaginary frequencies transverse to the reaction path; imaginary frequencies
may lead to unreliable or wrong results.
A limited amount of nontorsional anharmonicity may also be included, but a very
important feature of Polyrate is its ability to handle multistructural and torsional-potential
anharmonicity by utilizing the Polyrate in conjunction with the MSTOR program. See
Section 10.O.
The RP-VTST rate constants can be computed using canonical variational theory
(CVT), and microcanonical variational theory (VT). Conventional transition state theory
(TST) may also be employed. VRC-VTST calculations currently only can be applied to
gas-phase reactions using CVT, VT, and total energy and total angular momentum-
resolved microcanonical variational theory, which for short may be called E,J-resolved
microcanonical variational theory (E,J-VT).
For thermal or ground-state reactions using RP-VTST, tunneling probabilities can
be computed using the zero-curvature tunneling method (ZCT), the small-curvature
tunneling (SCT) method, the large-curvature tunneling (LCT) method, or an optimized
multidimensional tunneling method (OMT or COMT). The SCT calculations are based
on the centrifugal-dominant small-curvature semiclassical ground-state (CD-SCSAG)
method, and the LCT calculations are based on the large-curvature ground-state method,
version 3 or 4 (LCG3 or LCG4. For state-selected excited-state reactions only the ZCT
and SCT methods are available in this version. In addition, for ground-state reactions of
exoergic or thermoneutral reactions, LCT calculations may be summed over certain
excited final states, and for endoergic reactions, LCT calculations may be summed over
certain excited states of reactants. (These summations are a required part of the method
when these contributions are not negligible). The recommended tunneling procedure
when LCT calculations are carried out is the microcanonical optimized multidimensional
tunneling method (OMT) in which, at each energy, the tunneling probability is
Polyrate 16
approximated as the larger of the values calculated by the SCT and LCT methods. The
option of carrying out a tunneling calculation is not available in conjunction with VRC-
VTST option.
The Polyrate program computes rate constants by either single-level or dual-level
approaches for RP-VTST calculations and by single-level approach for VRC-VTST
calculations.
The single-level calculations and the lower level of dual-level calculations using
RP-VTST may be based on either an analytic potential energy function, which is called
the potential energy surface (PES) or potential energy function (PEF), or on various
types of interpolations of electronic structure input data at selected points along the
minimum energy path. VRC-VTST calculations can only be used for single-level
calculations based on a global PES or direct dynamics interfaced with an electronic
structure package.
When using a PES, the user must supply a subroutine, which, for a given set of
Cartesian coordinates of each of the atoms, returns the potential energy and its first
derivatives with respect to the Cartesian coordinates. This subroutine is called by a set of
Polyrate interface routines called hooks. (In particular, the “hooks” consist of
subprograms PREP, PREPJ, EHOOK, GHOOK, HHOOK, and OHOOK plus a few utilities, e.g.,
YTRANS and YNEWT, that are discussed in Section 8.C.). Note that VRC-VTST
calculations don’t need gradient information if optimized geometries and vibrational
frequencies of reactants and/or product are provided in the input file. When using
electronic structure input data without an analytic surface, the user must supply, as an
input file to the program, the geometries, energies, and force constants or frequencies for
the reactants, products, and saddle point, and optionally these quantities and the gradient
at a sequence of points on the minimum energy path. These data are then used for
dynamics calculations.
For RP-VTST calculations using dual-level approach, the data along the reaction
path may be “corrected” using higher-level data supplied by the user at selected points
either for reaction paths based on potential energy surfaces or for those based on
electronic structure input files. A generic name for such dual-level RP-VTST methods is
VTST-IOC. We currently recognize three variants of the IC methods, namely IOC
(interpolated optimized corrections), IOE (interpolated optimized energies), and ISPE
(interpolated single point energies). The IOC and IOE methods are also called triple-
slash (///) VTST. In the IOC method, the frequencies, potential energies, and moment-of-
inertia determinants along the reaction path that are calculated from the potential energy
surface are “corrected” using the results of higher-level electronic structure calculations
Polyrate 17
(supplied by the user) at selected points. The O in IOC indicates that any corrections at
stationary points are based on geometries optimized at the higher level. If corrections
were made at nonstationary points, they would be based on reaction paths calculated at
the higher level. The IOE approach is a subcase of IOC in which only the energies and
moment-of-inertia determinants are corrected, but the corrected energies are based on
geometries optimized at the higher level. The final dual-level method, called VTST-
ISPE, corrects only the energies along the reaction path using higher-level electronic
structure calculations (supplied by the user) at the stationary points and selected points
along the path. This kind of calculation is called a double-slash (//) calculation. In general
the acronyms VTST-IOC and VTST-IOE or the triple slash notation is reserved for cases
when the correction involves a higher-level geometry optimization of the transition state.
The VTST-ISPE notation refers to using higher-level single-point energies at the lower-
level saddle point or at the lower-level saddle point plus selected points along the lower-
level reaction path. Thus VTST-IOE is expected to be more accurate than VTST-ISPE,
even though one neglects the corrections to the frequencies.
In addition to the straight VTST method and to dual-level VTST-IOC and VTST-
ISPE, the code also has single-level IVTST options for RP-VTST calculations. With the
IVTST philosophy the user supplies the geometry, energy, and frequencies or Hessian at
the stationary points and additionally at as many points along the path as are
computationally feasible. Polyrate has the functionality to perform VTST calculations
with information at the stationary points and no points along the reaction path, called
IVTST-0, with one point along the path on either side of the saddle point, called IVTST-
1, or with an arbitrary number of points along the path on either side of the saddle point
(as long as there is at least one nonstationary point on either side of the saddle point).
The latter option is carried out by the mapped interpolation (MI) algorithm and is called
IVTST-M. In the current version of POLYRATE, IVTST-M is available with only the
default IVTST-M options when electronic structure input data is read from file fu30 or
fu40, and it is available with all the IVTST-M options for files fu31 and the hooks. Note
that IVTST-M can also be used as the lower level of a dual-level calculation, but in the
present version of Polyrate, IVTST-0 and IVTST-1 cannot be used that way.
In addition to the use of the MI algorithm as the central element of the IVTST-M
method with electronic structure input files, since version 8.0 of Polyrate we have
allowed the use of the MI algorithm as an "extrapolation" algorithm when using the
hooks for a calculation with a saddle point. If the hooks are used to interface with an
electronic structure calculation, this provides an alternative way to perform IVTST-M
direct dynamics calculations. If the hooks are used with an analytic potential, this
Polyrate 18
replaces the previously used method for extrapolating the adiabatic potential and
effective masses beyond the edge of the originally calculated grid. Finally we note that
the energy part of the MI algorithm is used in the VTST-ISPE version of VTST-IC.
There is also an option, called the RESTART option, in which the input consists in
part of reaction-path information calculated in a previous run of the program. The
RESTART option is not available for dual-level calculations.
Interface versions of POLYRATE, called CHARMMRATE, GAMESSPLUSRATE,
GAUSSRATE, JAGUARATE, MC-TINKERATE, MORATE, MULTILEVELRATE, and NWCHEMRATE,
which compute rate constants from potentials, gradients, and Hessians calculated by
electronic structure methods, are also available
CHARMMRATE is a module of the CHARMM program; CHARMMRATE can compute
enzyme-catalyzed rates by ensemble-averaged VTST. An interface to the CHARMMRATE
module of the CHARMM package based on Polyrate version 9.0, called CRATE, is available
as a separate distribution.
An interface to the GAMESSPLUS (or GAMESS) electronic structure packages based on
Polyrate version 9.3, called GAMESSPLUSRATE, is available as a separate distribution.
An interface to the GAUSSIAN16 (or GAUSSIAN98 or GAUSSIAN03 or GAUSSIAN09)
electronic structure packages based on Polyrate version 2017, called GAUSSRATE, is
available as a separate distribution.
An interface to the JAGUAR package based on Polyrate version 9.6, called
JAGUARATE, is available as a separate distribution.
An interface to the MC-TINKER package based on Polyrate version 9.1, called MC-
TINKERATE, is available as a separate distribution.
MORATE uses the semiempirical molecular orbital package MOPAC instead of an
analytic potential energy function. The electronic structure input file option and MORATE
are both examples of direct dynamics, i.e., rate or dynamics calculations based directly on
electronic structure information without the intermediary of an analytic fit to the potential
energy surface. The MORATE program is not distributed as part of the Polyrate package,
but it is available as a separate distribution from the University of Minnesota.
An interface to the MULTILEVEL package based on Polyrate version 9.1, called
MULTILEVELRATE, is available as a separate distribution.
An interface to the NWCHEM package based on Polyrate version 9.7, called
NWCHEMRATE, is available as a separate distribution.
AMSOLRATE is an interface with the AMSOL electronic structure package.
AMSOLRATE can also calculate rate constants for reactions in liquid-phase solutions.
AMSOLRATE can also be used for gas-phase calculations with semiempirical molecular
Polyrate 19
orbital theory, but we recommend MORATE for that purpose because it produces less
noisy frequencies. Therefore we do not mention AMSOLRATE in most lists of available
interface programs.
The various direct dynamics methods obtain their input about the system in
different ways:
• Single-level direct dynamics calculations may be carried out using file fu29,
file fu30, file fu31, file fu40, or file fu50 for the electronic structure
information (RP-VTST).
• VTST-IOC dual-level direct dynamics calculations may be carried out using
file fu30, fu31, or file fu40 for the lower-level information and file fu50 for
the higher-level information (RP-VTST).
• VTST-ISPE dual-level direct dynamics calculations may be carried out using
file fu30, fu31, or file fu40 for the lower-level information and file fu51 for
the higher-level information (RP-VTST).
• Single-level calculations based on an analytic potential energy surface obtain
the potential surface information from subprograms SETUP and SURF, which
are called by the hooks (RP-VTST and VRC-VTST).
• VTST-IOC dual-level calculations based on an analytic potential energy
surface for the lower level obtain the potential surface information from
subprograms SETUP and SURF (called by the hooks) and they obtain the higher-
level electronic structure information from file fu50 (RP-VTST).
• VTST-ISPE dual-level calculations based on an analytic potential energy
surface for the lower level obtain the potential surface information from
subprograms SETUP and SURF (called by the hooks) and they obtain the higher-
level electronic structure information from file fu51 (RP-VTST).
We note that files fu30, fu31, and fu40 accomplish essentially the same purpose.
There are two differences between fu30 and fu40 is that file fu30 requires formatted data,
whereas file fu40 is based on keyword input. The second difference is that there is a
WRITEFU30 keyword, but again there is no WRITEFU40 keyword. File fu31 is also based
on keyword input, but it differs from file fu40 in that certain IVTST-M options are
supported with fu31 but not with fu40. A second difference is that there is a WRITEFU31
keyword, but there is no WRITEFU40 keyword. See also Sect. 11.D.1. At some point in
the future we may stop supporting fu30, but for now we will keep it for the convenience
of users of previous versions. New users are encouraged to ignore fu30 and to use fu31
instead.
Throughout this manual it will be useful to keep in mind that there are really several
types of single-level VTST calculations, namely
1. Straight VTST
1.A. Straight VTST through the hooks
1.B. Straight VTST with file fu30 or file fu40
Polyrate 20
2. IVTST-M
2.A. IVTST-M with file fu30 or fu40
2.B. IVTST-M with file fu31
3. IVTST-0 or IVTST-1.
Note that RP-VTST calculations can be performed using any of these options, but
VRC-VTST calculations can only be performed using option 1.A. Calculations of type
1.A, 1.B, 2.A, and 2.B have many points of similarity, and in fact once Polyrate has all
the save grid arrays filled with data, these types of runs become identical. Further the MI
algorithm that constitutes the central element of IVTST-M calculations (2.A or 2.B) can
also be used in straight VTST (1.A or 1.B), but for straight VTST is considered as an
algorithm for extending the save grid to improve numerical convergence rather than
being considered as the main ingredient of the method. However runs of type 3 do not
use the save grid. In this manual we try to alert the reader whether a statement is true for
one or another of these types of calculations, but not for all four types. However, the
reader should be aware that sometimes we fail to mention this because it is assumed clear
from the context or because the manual needs more work.
Dual-level calculations can be performed with type 1.A, 1.B, 2.A, or 2.B
calculations as the lower level.
The main options for RP-VTST calculations are summarized in the following table:
Polyrate 21
Dynamics
approach
hooks fu29 fu30, fu31, or
fu40
fu50
TST TST TST TST TST
VTST TST/ZCT
CVT
CVT/ZCT
CVT/SCT
CVT/LCT
VT
VT/ZCT
VT/SCT
VT/LCT
TST/ZCT
CVT
CVT/ZCT
CVT/SCT
VT
VT/ZCT
VT/SCT
IVTST-0 TST
TST/ZCT
TST
TST/ZCT
IVTST-1 TST
TST/ZCT
CVT
CVT/ZCT
CVT/SCT
hooks
plus fu50
fu30, fu31, or
fu40 plus fu50
VTST-IOC TST
TST/ZCT
CVT
CVT/ZCT
CVT/SCT
CVT/LCT
TST
TST/ZCT
CVT
CVT/ZCT
CVT/SCT
Polyrate 22
Table continued:
Dynamics
approach
hooks
plus fu50
fu30, fu31, or
fu40 plus fu50
VTST-IOC VT
VT/ZCT
VT/SCT
VT/LCT
VT
VT/ZCT
VT/SCT
hooks
plus fu51
fu30, fu31, or
fu40 plus fu51
VTST-ISPE VT
VT/ZCT
VT/SCT
VT
VT/ZCT
VT/SCT
Note that whenever both SCT and LCT methods are available, then the µOMT method is
available as well.
Also note: When an analytical potential is used, the hooks call SETUP and SURF.
However, the hooks capability is more general, and the hooks can be used to interface
Polyrate with electronic structure codes for direct dynamics; examples are the CRATE,
GAMESSPLUSRATE, GAUSSRATE, JAGUARATE, MC-TINKERATE, MORATE, MULTILEVELRATE,
and NWCHMERATE programs, which are interfaces to CHARMM with the CHARMMRATE
module, GAMESSPLUS, GAUSSIAN, JAGUAR, MC-TINKER, MOPAC, MULTILEVEL, and
NWCHEM, respectively.
Polyrate 23
2. RECOMMENDED CITATION FOR POLYRATE 17-C
The recommended CITATION for the Polyrate code is
J. Zheng, J. L. Bao, R. Meana-Pañeda, S. Zhang, B. J. Lynch, J. C. Corchado, Y.-Y.
Chuang, P. L. Fast, W.-P. Hu, Y.-P. Liu, G. C. Lynch, K. A. Nguyen, C. F. Jackels,
A. Fernandez Ramos, B. A. Ellingson, V. S. Melissas, J. Villà, I. Rossi, E. L. Coitiño, J.
Pu, T. V. Albu, A. Ratkiewicz, R. Steckler, B. C. Garrett, A. D. Isaacson, and
D. G. Truhlar, Polyrate 17-C, University of Minnesota, Minneapolis, 2018.
https://comp.chem.umn.edu/polyrate/
References for methods used in the code are given in Sect. 21 of this manual.
3. RECOMMENDED CITATIONS FOR INCORPORATED CODE
1. The code for evaluating the Cartesian B matrix and C tensor for stretches,
nondegenerate bends, and torsions for the general polyatomic case is from J.
Cioslowski and M. Challacombe, ANHTRAX, QCPE Program No. 609 (Quantum
Chemistry Program Exchange, Bloomington, IN, 1991). (used with permission)
2. The EF code for stationary point optimization is from J. Barker, F. Jensen, H. S. Rzepa,
A. Stebbings, LOCATION OF TRANSITION STATES IN AMPAC AND MOPAC USING
EIGENVECTOR FOLLOWING (EF), QCPE Program No. 597 (Quantum Chemistry Program
Exchange, Bloomington, IN, 1990). (used with permission)
Polyrate 24
4. LICENSING
Polyrate 17-C is licensed under the Apache License, Version 2.0.
The manual of Polyrate 17-C is licensed under CC-BY-4.0.
Publications of results obtained with the Polyrate 17-C software should cite the program
and/or the article describing the program.
No guarantee is made that this software is bug-free or suitable for specific applications,
and no liability is accepted for any limitations in the mathematical methods and
algorithms used within. No consulting or maintenance services are guaranteed or implied.
The use of the Polyrate 17-C implies acceptance of the terms of the licenses.
Polyrate 25
5. PROGRAM AND MANUAL DESCRIPTION
5.A. Code description, portability, and special files
The Polyrate program is written in FORTRAN 90 with the module and dynamically
allocated memory features.
Users should be aware that, beginning with version 2008, Polyrate can perform two kinds
of calculations. One is RP-VTST, and the other one is VRC-VTST, as explained in
Section 1. These two kinds of calculations involve different subroutines to generate
different executable programs. RP-VTST has both serial and MPI parallel versions and
VRC-VTST has only an MPI parallel version and requires one to link to the SPRNG
library. Starting with version 2010, the SPRNG package is included in the Polyrate
distribution for the user’s convenience, and the Polyrate installation script includes
compiling the SPRGN library before linking Polyrate subroutines to this library.
Therefore installation of SPRNG library and Polyrate program can be done with one
script. To use RP-VTST, no pre-installed library or package is required.
The SPRNG package can be also obtained separately from the web page:
http://sprng.cs.fsu.edu/
5.B. Description of the manual
This manual is divided into five parts.
Part I has five sections and includes general information about POLYRATE.
Part II has five sections and includes theoretical background and computational details
for RP-VTST. Section 6 provides an overview of theoretical background for the
dynamical calculations. Section 7 gives information related to the program structure.
Sections 8 and 9 describe the calculations using a potential energy surface (Section 8) or
direct dynamics calculations, which use an electronic structure input file (Section 9).
Section 10 provides selected details of the calculations, especially for procedures that are
not fully described in publications.
Polyrate 26
Part III has one section, Section 11, to describe the theoretical background of VRC-
VTST.
Part IV has 3 sections for description of input files. Section 12 describes the complete
Polyrate input and selected aspects of the output for RP-VTST calculations. Section 13
describes the input file for VRC-VTST. Section 14 describes files that give extra details
of LCT calculations.
Part V gives more general information about the Polyrate program package. Section 15
contains instructions on how to install, test, and use the Polyrate program. Section 16
gives sample runs (the Polyrate test suite) that may be useful in understanding the input
or testing the program. Section 17 lists the files in the program distribution, and it has a
brief explanation of each subprogram. Section 18 contains instructions on using the Unix
scripts that are provided. Section 19 describes file usage. Section 20 provides references
indicated by brackets in the text of the manual, and Section 21 is the Polyrate
bibliography.
Much of the mathematical formulation underlying the dynamical calculations is presented
in a book chapter entitled “Variational Transition State Theory with Multidimensional
Tunneling,” which is Ref. 71 in the bibliography (Sect. 21), and should be consulted
along with this manual. “Generalized Transition State Theory“ (GTST), which is Ref. 5
in Sect. 21, is also a useful chapter, especially for an introduction to the older core ideas,
although Ref. 71 supersedes it. If these books are unavailable in your library, you may
obtain a copy of the chapters from the senior author (DGT) at
http://comp.chem.umn.edu/Polyrate
A PDF file with a complete compilation of all known errors in Ref. 5 is also given at this
Web site.
5.B.1. Referencing conventions
Reference numbers in this manual refer to references in Sect. 20. In all cases the
reference number is accompanied by the section number to avoid confusion.
Polyrate 27
5.B.2. Key references
Reference 5 in Sect. 21 is sometimes referred to simply as "the GTST book chapter":
“Generalized Transition State Theory”, D. G. Truhlar, A. D. Isaacson,
and B. C. Garrett, in The Theory of Chemical Reaction Dynamics, edited
by M. Baer (CRC Press, Boca Raton, FL, 1985), Vol. 4, pp. 65-137.
Reference 71 in Sect. 21 is sometimes referred to as “the VTST/MT book chapter”:
"Variational Transition State Theory with Multidimensional Tunneling,"
A. Fernandez-Ramos, B. A. Ellingson, B. C. Garrett, and D. G. Truhlar,
in Reviews in Computational Chemistry, Vol. 23, edited by K. B.
Lipkowitz and T. R. Cundari (Wiley-VCH, Hoboken, NJ, 2007), pp.
125-232.
These two book chapters explain the methods used in Polyrate up to 2005. PDF files of
these chapters are available at the Polyrate Web site:
http://comp.chem.umn.edu/polyrate
All known errata to the GTST book chapter have been assembled into a PDF file. This
file is also available at the Polyrate Web site.
A review that also covers the more recently developed methods is also available: Ref.
114 in Sect. 21:
“Variational Transition State Theory: Theoretical Framework and
Recent Developments,” J. L. Bao and D. G. Truhlar, Chemical Society
Reviews 46, 7548-7596 (2017). doi.org/10.1039/C7CS00602K
Taken together, these three articles explain almost all the methods used in Polyrate.
Polyrate 28
Part II Theory Background and Calculation Details on RP-VTST
6. THEORETICAL BACKGROUND ON RP-VTST
This section provides an overview of the dynamical theory underlying the calculation
procedures. Further details of the methods for gas-phase bimolecular and unimolecular
reactions may be found in the "Generalized Transition State Theory" (GTST) book
chapter (Ref. 5, Sect. 21). Details of new methods developed after that chapter was
written are described in Section 10 of this manual, if not fully published, or in the
additional references in Sect. 21, especially the VTST/MT book chapter (Ref. 70 of Sect.
21) and the most recent review (Ref. 114 of Sect 21).
6.A. Basic theory
As described in the Introduction, the program can be used to calculate rate constants for
reactions of one or two reactant molecules to form one or two product molecules, using a
variety of generalized transition state theory methods. In order to simplify the
discussions in the remainder of this introductory overview section, we consider only the
calculation of forward and reverse thermal rates using both conventional transition state
theory (TST) and canonical variational theory (CVT). Microcanonical variational theory
(µVT) are described in detail in the GTST book chapter. The applications of VTST
methods to gas-phase unimolecular or bimolecular reactions or gas-solid-interface
reactions or the calculation of adiabatic and diabatic state-selected rate constants are
described in the references included in Sect. 21.
The improved canonical variational theory (ICVT) option has been removed from
Polyrate. If one sees a need for the more accurate threshold treatment of ICVT, one
should instead use µVT because µVT is coded in Polyrate with the extended Beyer-
Schwinehart (BS) algorithmfor calculating number of available state, and this iss more
efficient and more complete than IVCT.
The conventional transition-state-theory canonical rate constant involves a symmetry
number [Ref. 1, Sect. 22] times kT/h times a ratio of a partition function evaluated at the
saddle point to one evaluated at the reactants, and, optionally, times a temperature-
Polyrate 29
dependent transmission coefficient, which in this program, takes into account tunneling
and non-classical reflection effects. The partition functions are evaluated as products of
electronic, vibrational, and rotational partition functions, and for the reactants of a
bimolecular reaction, a relative translational partition function per unit volume. In
Polyrate, vibrational partition functions are defined such that they tend to a Boltzmann
factor of the zero point energy at low temperature (not to unity as is common in statistical
mechanics books), and the corresponding local zero of energy is used consistently for the
rest of the calculations.
To calculate rate constants by the CVT method various items of information are needed
along the reaction path. In Polyrate, the reaction path is always taken as the minimum
energy path (MEP) through mass-scaled (i.e. isoinertial) coordinates [Refs. 2-5, Sect. 22]
except for the treatment of loose transition state using variable-reaction-coordinate
(VRC) algorithm with single-faceted or multifaceted (MF) dividing surface (the VRC
algorithm and MF dividing surfaces are discussed in detail in Section 11). The
descriptions here are all referred to MEP. Following Fukui [Ref. 5, Sect. 22], one may
call this the "intrinsic" reaction path. (In Polyrate, we always call it the MEP.) The
distance along the MEP is called s, or the reaction coordinate. For reactions with a saddle
point, the MEP is specifically defined to be the path of steepest descent through mass-
scaled Cartesian coordinates from the saddle point (s = 0) to the reactants (at which s
= – for a bimolecular reaction, or s equals a finite negative number for a unimolecular
reaction) and the path from this saddle point to the products (at which s = + for a
bimolecular reaction, or s equals a finite positive number for a unimolecular product).
We define a sequence of generalized transition states corresponding to the reaction
coordinate to be hypersurfaces which are orthogonal to the MEP [Ref. 6, Sect. 22]. All
quantities calculated for a generalized transition state that intersects the MEP at a
particular value s of the reaction coordinate are labeled by that value of s (as well as the
temperature T when they depend on temperature). The generalized TST canonical
forward rate constant
kfGT(T,s) is then evaluated like the conventional one but with
saddle point properties replaced by generalized transition-state (GT) ones. Thus, at each
generalized transition state along the reaction path the following information is (or may
be, depending on the options chosen) needed:
VMEP(s) — potential along the minimum energy path,
|I(s)| — determinant of the moment of inertia tensor,
Polyrate 30
X(s) — geometry of the generalized transition state,
— the gradient of the generalized transition state,
Lm(s) — eigenvector of the generalized normal mode m,
wm(s) — generalized normal mode frequencies.
In addition, depending on the anharmonicity option and the method chosen to include
tunneling, one may also require some or all of the following additional functions:
km(3)(s) — principal cubic force constants for the generalized normal
modes,
km(4)(s) — principal quartic force constants for the generalized normal
modes,
BmF(s) — reaction-path curvature coupling [Ref. 7, Sect. 22] between
the reaction coordinate (mode F) and generalized normal
mode m. Sometimes we refer to the set of BmF(s) with m=1,
2, ..., F-1, as the curvature vector BF.
Note that “principal” force constants are diagonal in the normal mode index; that is why
k3(s) and k4(s) are short one-dimensional arrays. The functions listed above and the
reaction path itself can be obtained through the hooks, which can in turn be interfaced to
an analytic potential energy surface or an electronic structure package, or alternatively
this data (or information which can be used to calculate this data) can be obtained from
electronic structure calculations carried out separately from Polyrate. In the latter case
the MEP information is input only on a relatively sparse grid of s values, and the program
interpolates this information to arbitrary s values. This option is called the electronic
structure input file option (POTENTIAL = unit30, unit31, or unit40).
The isoinertial coordinate system used by Polyrate is defined by eq. (2) of Ref. 1 of Sect.
21 or, equivalently, by eq. (2) of Ref. 5 of Sect. 21. These coordinate systems have the
same reduced mass, µ, for all degrees of freedom. Physical observables and the MEP are
independent of µ, but numerical values of s are not. Thus it is essential to specify if s
values or plots of barriers vs. s are considered. If is set equal to 1 amu, then the
numerical value of s in mass-scaled coordinates (which have units of length) is the same
as the numerical value of the distance along the usual spectroscopists’ mass-weighted
coordinates (which have units of mass 1/2 length) if the mass weighting is amu1/2.
Polyrate 31
Therefore setting equal to 1 amu procedure is especially recommended if the goal is to
make the treatment transparent to those who are only used to the spectroscopists’ mass
weighting scheme.
The reverse rate constant is obtained from the forward one by detailed balance. The
canonical variational theory [Ref. 6, Sect. 22] forward rate constant is obtained by
minimizing the generalized transition state theory rate constant with respect to s:
k fCVT T( ) = min
sk f
GT T,s( ) = k fGT T,s*
CVT T( )[ ] (1)
Generalized-transition-state-theory rate constants can also be written in terms of the
generalized transition-state (GT), standard-state (0), forward (f) free energy of activation,
. The location of the variational transition state is then determined by
maximizing the free energy of activation with respect to s.
Section 6.C gives a brief explanation of the evaluation of the partition functions and
Section 6.D summarizes methods used for transmission coefficients.
6.B. Vibrations, Rotations, and Translations
This section gives a brief explanation of how Polyrate uses the SPECIES keyword (see
Section 12.A.6) to determine the number of rotations and vibrations used in calculating
the partition functions and the number of degrees of freedom which are projected out by
the projection operator (when the PROJECT option is on, see Section 12.A.6) for the given
reactant, product, transition state, or generalized transition state. The table below gives
the valid values of the SPECIES keyword and a description of what the values mean, along
with the number of vibrations and rotations in the partition function for each type of
species, and the number of modes which are projected out to remove translations,
rotations, and the reaction coordinate.
Polyrate 32
Description SPECIES
keyword value
Partition Function Projection Operator
Vibrations Rotations Translations Rotations Reaction
Coordinate
Mandatory?
atomic
reactant or
product
atomic 0 0 … … … N.A.
linear
reactant or
product
linrp 3N – 5 2 3 2 0 optional
nonlinear
reactant or
product
nonlinrp 3N – 6 3 3 3 0 optional
solid-state
reactant or
product
ssrp 3N 0 0 0 0 prohibited
linear
transition
state
lints 3N – 6 2 3 2 0 optional
nonlinear
transition
state
nonlints 3N – 7 3 3 3 0 optional
solid-state
transition
state
ssts 3N – 1 0 0 0 0 prohibited
linear GTS N.A. 3N – 6 2 3 2 1 mandatory
nonlinear
GTS
N.A. 3N – 7 3 3 3 1 mandatory
solid-state
GTS
N.A. 3N – 1 0 0 0 1 mandatory
N.A., Not Applicable; N, number of atoms
Polyrate 33
For an atomic reactant or product the value atomic should be specified for SPECIES.
Since the species is a single atom there are no vibrations or rotations, nor is there any
Hessian to consider projecting. Therefore the PROJECT keyword (see Section 12.A.6)
cannot be used with an atomic species.
Gas-phase reactants and products that are not atomic and transition states can be either
linear or nonlinear, specified by linrp, nonlinrp, lints, and nonlints
respectively. After removing the 2 rotations and three translations for a linear molecule
there are 3N – 5 vibrations for the linear species, and after removing the 3 rotations and 3
translations for a nonlinear molecule there are 3N – 6 vibrations for a nonlinear species.
A gas-phase transition state has one additional mode removed due to the reaction
coordinate and therefore has 3N – 6 real vibrations for a linear molecule and 3N – 7 real
vibrations for a nonlinear molecule. The number of vibrations for a generalized transition
state is calculated in the same manner as for a conventional transition state (which is a
saddle point, also called a transition structure). Projecting the Hessian at a transition state
is not required, but sometimes it leads to a more stable calculation of vibrational
frequencies and eigenvectors, so it is a recommended option to project out translations
and rotations at a reactant, product, or transition state. For generalized transition states
(points on the reaction path where the gradient does not vanish), projecting out the
reaction coordinate is mandatory if the resulting frequencies are to represent motions
orthogonal to the reaction coordinate. In such cases it is also mandatory to project out
translations and rotations, if they exist (they always exist for gas-phase cases, but not for
solid-state cases).
Solid-state species are different than gas-phase species as concerns the number of
vibrations. For solid state species there are no rotations or translations which are
removed because a rotation or a translation of a species relative to a surface changes the
potential energy of the whole system. Therefore there are 3N vibrations for a reactant or
product species and 3N – 1 for a transition state or generalized transition state species.
The reaction coordinate is removed for a solid-state species in the same manner as it is
for a gas-phase species.
Polyrate 34
6.C. Partition functions
The electronic partition function for a given species is computed quantum mechanically
by summing over the Boltzmann factors of the electronic energy levels of the species
times their degeneracies. In practice, since the energy spacing between electronic
multiplets is generally quite large, we usually include in the summation only those levels
comprising the energetically lowest multiplet, e.g., the J = 0, 1, and 2 levels of O(3P).
The rotational partition function is approximated by the classical limit [Refs. 8 and 9,
Sect. 22]. For a linear reactant, product, transition state, or generalized transition state,
the partition function is evaluated from the unique moment of inertia. For a nonlinear
species, the product of the three principal moments of inertia is required and is
conveniently obtained from the determinant of the moment of inertia tensor. All
symmetry numbers are left out of all rotational partition functions; the symmetry numbers
need only to be included in the overall symmetry number mentioned above [Ref. 1, Sect.
22].
For bimolecular reactions, the relative translational partition function per unit volume is
calculated classically.
For vibrational partition functions, a separable approximation is assumed, whereby the
overall vibrational partition function is a product of independent normal modes of a
reactant, product, or saddle point or the generalized normal modes of a generalized
transition state. Vibrational modes are treated classically or quantized, either quantum
mechanically or semiclassically. Anharmonic methods are limited to intramode
anharmonicity in normal modes expressed as linear combinations of rectilinear
coordinates and do not include mode-mode coupling as a supported option at this time.
The torsional potential anharmonicity along reaction path can be included using the
formula of the multi-structural torsional method but only with one input structure.
Classical vibrational partition functions are evaluated using the classical expression for
the harmonic oscillator. Quantum mechanical vibrational partition functions are
evaluated by the harmonic approximation, by summing Boltzmann factors using quantum
or semiclassical energy levels.
Polyrate 35
Frequencies can be scaled for partition function calculations in CVT calculations when
the harmonic approximation is employed. The scaling is not used in the calculation of
transmission coefficients (either by CAG or tunneling).
6.D. Tunneling methods
Different semiclassical methods are used to evaluate transmission coefficients depending
on the degree of coupling between the MEP and other degrees of freedom through the
MEP curvature. There are three general types of transmission coefficients:
zero-curvature tunneling (ZCT), small-curvature tunneling (SCT) and large-curvature
tunneling (LCT). The methods included in this version for each type of transmission
coefficient for thermal reactions are as follows:
ZCT: minimum-energy-path semiclassical adiabatic ground-state
(MEPSAG) method [Refs. 4 and 10, Sect. 22 and Ref. 5, Sect. 21].
SCT: centrifugal-dominant small-curvature semiclassical adiabatic
ground-state (CD-SCSAG) method [Refs. 29 and 31, Sect. 21].
LCT: large-curvature ground-state version-3 (LCG3) method [Refs. 5, 21,
29, 30, and 34, Sect. 21] and large-curvature ground-state version-4
(LCG4) method [Ref. 54, Sect. 21].
The current theory of these tunneling methods appears in “Variational Transition State
Theory with Multidimensional Tunneling,” which is Ref. 59. The final version
(CD-SCSAG, which replaced the original SCSAG) of the SCT method is described in
Refs. 29 and 31 in Sect. 21, and the final versions of the LCT method are described in
Refs. 29, 30, 34 (LCG3 including tunneling into excited states), and Ref. 54 (LCG4
including tunneling into excited states) in Sect. 21. The final versions of these methods
were used in all references of Sect. 21 that have reference number 30 or higher. A
critical element of the SCT calculation is that the reduced mass, (See Section 6.A), is
replaced by an effective mass meff s( ) in calculating the tunneling probabilities. See
Section 6.I of this manual for further discussion.
Notice that the G in MEPSAG, CD-SCSAG, LCG3, and LCG4 refers to the fact that the
transmission coefficient for thermal reactions is always calculated for the ground (G)
state of the reactants in the exoergic direction of a reaction, as discussed elsewhere (Ref.
[13] Sect. 22 and Refs. 29, 30, and 34 of Sect. 21). The transmission coefficient for the
Polyrate 36
endoergic direction of a reaction is then obtained by detailed balance, which requires that
the transmission coefficients for thermal reactions be the same in both directions. The
LCG3 and LCG4 methods can include tunneling into excited states of the product in the
exoergic direction, and the algorithm in Polyrate is general enough to treat even cases
that involve a well on the product side in the exoergic direction. (Wells on the reactant
side do not require special considerations in this regard.) The ground-state
approximation for the transmission coefficient is equivalent to assuming that the energy-
dependent transmission probability curve for each successive quantized level of the
transition state has the same functional dependence on energy as that for the ground state
but is shifted up in energy by the excitation energy evaluated at the variational transition
state [Ref. 47, Sect. 22].
When reaction-path curvature is large, it may be necessary to include excited states of the
product of the exothermic direction in order to obtain accurate results, and the user of
Polyrate is responsible for checking this by checking convergence with respect to the
argument of the EXCITED keyword in the TUNNEL section.
VTST methods are also applicable to state-selected reactants if the quantum number of
the selected mode remains adiabatic, to a good approximation, all the way to the
transition state. Excited-state tunneling probabilities may be defined using similar
methods to those mentioned above, and they are called MEPSA, CD-SCSA, and LC3 or
LC4, i.e., we don't include the G when the method is applied to excited states of reactants.
These abbreviations and the ZCT, SCT, and LCT abbreviations are also useful when we
wish to refer to the semiclassical method without reference to the initial state. The
present version of Polyrate allows the MEPSA and CD-SCSA options for excited-state
reactions but does not allow LC3 or LC4, which is not coded in such generality.
Regions of large reaction-path curvature can promote vibrational nonadiabaticity. The
partial-reaction-path (PRP) adiabaticity approximation [Ref. 13A, Sect 21] assumes
adiabaticity in the excited-state vibration up to the first point along the reaction
coordinate where an appreciable local maximum in the reaction-path curvature occurs,
which we denote s+. The vibration is assumed to relax nonadiabatically into the ground
vibrational state after s+. The adiabatic potential for tunneling is the excited-state one up
to s+ and the ground-state one for s>s+. Excited-state PRP calculations can be
implemented using the STATE and STATEOPT keywords in the RATE section. An
example of an excited-state PRP calculation is provided in test run ohcltr4.
Polyrate 37
The multidimensional tunneling methods used in Polyrate have been tested extensively
against accurate quantal results [Ref. 53, Sect 20].
6.E. Reactant and product properties
The first step in the calculation is to determine the properties of the reactants and
products. We will specifically discuss reactant A (the first reactant, which may be an
atom or molecule) as an example in this subsection; the methods for the other reactant, in
the case of a bimolecular reaction, or for products are analogous.
The calculation begins by determining the equilibrium geometry and energy for reactant
A on the potential energy surface. The reactant geometry is optimized by using either the
Newton-Raphson (NR) method with Brent line minimization [Ref. 14, Sect. 22], the
Broyden-Fletcher-Goldfarb-Shanno (BFGS) method [Ref. 15, Sect. 22], or the
Eigenvector Following (EF) method [Refs. 54-58, Sect. 22] to search over a restricted set
of atomic Cartesians coordinates. These options are not available for the program
packages MORATE and AMSOLRATE, in which the geometry optimization is only carried
out in the electronic structure program (which is specified using option HOOK). To do
this, the user must fix (somewhat arbitrarily) 6 of the Cartesian coordinates (5 for a linear
species) and search over the rest. For example, the user might fix atom 1 at the origin,
atom 2 on the x-axis, and the atom 3 in the x-y plane. (In the case of solid-state or gas-
solid-interface reactions, there are no translations or rotations because the moving atoms
are adsorbed on or embedded in a stationary lattice; thus for such cases, the full set of
atomic Cartesians of the movable atoms is used). Starting from an initial guess, an
improved estimate for the position of the minimum is obtained by taking a step ,
where is obtained by solving a simultaneous set of equations (given in the GTST
book chapter) involving the matrix of second derivatives of the potential energy and the
gradient. Once is obtained by direct calculation of the inverse Hessian matrix (NR
method) or estimated using information from the previous geometry optimization steps
(BFGS method), a new guess for the position of the minimum is obtained using either the
NR step or a variable step size which is determined by the Brent line minimization
method [Ref. 16, Sect. 22] (BFGS method). For the EF method, the step is determined
by the hessian. If the hessian has the wrong number of negative eigenvalue, then the
partitioned rational function (P-RFO) approximation is used. If the hessian has one
Polyrate 38
negative eigenvalue, then Newton-Raphson step is used. The detailed EF algorithm is
given in [Ref. 56, Sect. 22].
For all methods, convergence is reached when the maximum component of the gradient
in the space of optimized coordinates is less than a prescribed amount GCOMP. In order to
increase the stability of the optimization, the maximum component of the step, DR0 , is
not allowed to be larger than the prescribed amount SCALE for the NR and BFGS
methods. However, the SCALE keyword has no effect on the EF method. The accurate
Hessian is recalculated every HREC optimization steps. In the case of the NR method, if
HREC is not equal to 1, the Hessian is kept frozen until recalculated. The BFGS method is
the default. The EF method has a few extra options, namely, RMAX, RMIN, OMIN, DDMAX,
and DDMAXTS, to control the size of the trust region and tune up the optimization
procedure.
Next, the origin is moved to the center of mass of reactant A. The moment of inertia or
the product of the principal moments of inertia is then determined. Finally, a normal
mode analysis is performed on reactant A. Since, in mass-scaled Cartesians, motion in
any direction is associated with the same reduced mass (that is why we call these
isoinertial coordinates), this is easily accomplished by diagonalizing the force constant
matrix. The force constant matrix is calculated by numerical first derivatives of the
analytic or input first derivatives of the potential. In the case of gas-phase reactions, we
can optionally project out the contamination of the translational and rotational motions in
the force constant matrix at the stationary point before diagonalizing it to yield 6 zero
eigenvalues (5 for a linear molecule) corresponding to overall translation and rotation.
The remaining eigenvalues are all positive, corresponding to bound normal mode
frequencies, and their associated (normalized) eigenvectors Lm give the normal mode
directions. After the frequencies are calculated, the frequencies and corresponding
eigenvectors are placed in “canonical order.” Canonical order is defined as follows:
First define G:
Stationary point: G = R + T = 6 for nonlinear molecule,
5 for linear molecule,
0 for gas-solid interface.
Reaction path: G = R + T + 1
Then the frequencies are ordered as follows:
1. The G frequencies with the smallest absolute values go last, ordered in
order of decreasing magnitude.
Polyrate 39
2. Of the remaining frequencies, first put the real ones, in decreasing
order, then put the imaginary ones, in order of increasing magnitude.
By computing or reading the third and fourth derivatives of the potential energy along
these normal mode directions, anharmonicity may be included separately in each of the
modes, as discussed elsewhere [Ref. 1, Sect. 21]. Depending on the method chosen for
treating the anharmonicity, the zero point energy is then computed for reactant A by
summing up the zero point energies in each of the normal modes.
The calculations in this section are then repeated for the other reactant (if it exists) and
for product(s). From these results, the adiabatic energy of reactants, the classical
endoergicity for the reaction, E, and the product adiabatic energy are obtained.
Notice that the normal mode analysis can only be carried in rectilinear coordinates for
reactants and products, whereas the saddle point and the nonstationary points can be
treated either in rectilinear or in curvilinear coordinates. (It is very important to use
curvilinear coordinates rather than Cartesian coordinates for VTST calculations;
Cartesian coordinate will very likely yield imaginary frequencies along the reaction
coordinate, which will cause unphysical VTST results.)
6.F. Saddle point properties
The calculation of the saddle point geometry and properties is next. The saddle point
position is determined by means of the Newton-Raphson method, the BFGS method, or
the EF method as described in Subsection 6.E. The default for transition state searches is
the Newton-Raphson method. This optimization provides the saddle point’s classical
barrier height VMEP (s = 0). Next, the origin is moved to the center of mass of the full N-
atom system. The moment of inertia is obtained as discussed for reactants. Next the
force constant matrix is calculated in mass-scaled Cartesians, and optionally the
contributions of the overall translational and rotational motions are projected out. The
normal mode analysis can be carried out in either the rectilinear or curvilinear
coordinates for the saddle point. (It is very important to use curvilinear coordinates rather
than Cartesian coordinates for VTST calculations; Cartesian coordinate will very likely
yield imaginary frequencies along the reaction coordinate, which will cause unphysical
VTST results.) In the case of using rectilinear coordinates, a diagonalization of the 3N
3N matrix of force constants in mass-scaled Cartesian coordinates is performed. Upon
Polyrate 40
diagonalization, we again obtain 6 zero eigenvalues (5 for a linear molecule, 0 for solid
state), 3N-7 (3N-6 or 3N-1) positive eigenvalues corresponding to bound normal mode
frequencies, and one negative eigenvalue corresponding to the imaginary frequency
whose eigenvector provides the reaction coordinate direction at the saddle point. After
the frequencies are calculated, the frequencies and corresponding eigenvectors are placed
in canonical order (which is defined in Section 6.E). The imaginary frequency is used at
a later stage to compute the Wigner tunneling correction (see Subsection 6.J). By
computing or reading the third and fourth derivatives along the normal mode directions
as discussed above, anharmonicity can be included separately in each of the 3N-7 (3N-6
for a linear molecule, or 3N-1 for solid state) bound normal modes (see Subsection 10.B
of this manual), and the zero point energy (ZPE) for the transition state is computed from
the sum of the zero point energies of each of the modes. The ground-state adiabatic
energy at the saddle point is then calculated as:
Va
G s = 0( ) =Va n = 0, s = 0( ) =VMEP(s = 0)+ ZPE(s = 0) (2)
The normal mode analysis can also be carried using redundant (or nonredundant)
curvilinear coordinates. In this case, Wilson’s FG matrix method is used to obtain the
projected force constant matrix in internal coordinates. See Section 10.L. for further
discussion of curvilinear internal coordinates.
6.G. Reaction path
In this section, we discuss how the reaction path (or, more precisely, a set of points along
an approximation to the reaction path) and various properties along it are determined. In
the present version of Polyrate, the reaction path is always taken as the minimum-energy
path (i.e. the path of steepest descents) in mass-scaled coordinates; this is called the MEP.
Note that the path of steepest descent is the same in any isoinertial coordinate system.
[Ref. 49, Sect. 22] There are four cases, and the current version of Polyrate allows three
of them:
In START In PATH
STATUS = 0
SADDLE
Reaction has a saddle point. Initial guess of its
geometry is provided in the START section of the fu5
input file. The geometry of the saddle point is
optimized. The first step is followed along the
imaginary frequency normal mode (if FIRSTSTEP is
Polyrate 41
nmode) or with the cubic starting algorithm based on
this mode (if FIRSTSTEP is cubic).
STATUS = 2
SADDLE
This is the same as above except it assumes that the
geometry in the START section is already fully
optimized, and it skips the optimization step.
STATUS = 0 NOSADDLE Not supported.
STATUS = 2
NOSADDLE
Reaction does not have a saddle point. It is a strictly
downhill association reaction. The reaction path is
started by following the negative gradient at the
geometry provided in the START section.
Most of the test runs in the current version of Polyrate correspond to STATUS = 0/SADDLE.
An example of STATUS = 2/SADDLE is test run oh3tr1. All fu29, fu30, fu31, and fu40 test
runs use STATUS = 2/SADDLE. An example of STATUS = 2/NOSADDLE is ho2tr2.
6.G.1. SADDLE option
Taking the saddle point as the first point on the reaction path, an initial step of prescribed
length is taken according to one of two options. Either it is taken based on a cubic
expansion of the potential energy surface [Ref. 17, Sect. 22] using the normalized
eigenvector corresponding to the imaginary frequency and the curvature vector, both of
which are calculated at the saddle point, or it is taken in the direction given solely by the
normalized eigenvector corresponding to the imaginary-frequency normal mode at the
saddle point, as was done in the original version of the program [Ref. 1, Sect. 21]
described in the GTST book chapter.
In the original straight VTST calculations [Ref. 18, Sect. 22; Ref. 1, Sect. 21] the MEP
was calculated by the Euler steepest-descents (ESD) method in which repeated steps of
length s are then taken in the direction of the negative of the normalized gradient. The
whole process is then repeated for the other direction of leaving the saddle point, thus
providing the entire reaction path. The distance between successive points along the
reaction path (s) is called the reaction path stride or the gradient step size, and the set of
such points is called the fine grid or the gradient grid. Thus, at each point on the fine grid
both the potential and gradient are required.
Polyrate 42
To reduce the numerical error in the above approach due to wandering about the true
steepest-descent path, the program allows for a stabilization algorithm to be employed.
This algorithm [Ref. 18, Sect. 21] may be considered to be a modified version of the
prescriptions of Ishida et al. [Ref. 19, Sect. 22] and Schmidt et al. [Ref. 20, Sect. 22]. It
is called ES1 (Euler stabilization method, version 1), and it is described elsewhere [Ref.
18, Sect. 22]. In the original version of the ES1 algorithm, the stabilization step was
omitted whenever the vector difference between successive normalized gradients was less
than 10-8, but now this is only a default value and the user is free to choose among other
possible values which might be more appropriate for the reacting system under study.
This is controlled by the keyword DIFFD.
The ES1 method involves two auxiliary parameters, the stabilization step size DELTA2
and the tolerance in the allowed magnitude DIFFD of the vector difference between
successive normalized gradients, and the accuracy achieved for a given amount of
computer time can be sensitive to these values. These values have been approximately
optimized in a systematic study of methods for calculating minimum energy paths (see
Ref. 27 in Sect. 21). In that study, "standard" values were determined for both
parameters. These "standard" values are: a) the stabilization step size DELTA2 equal to
the gradient step size SSTEP, and b) the tolerance in the allowed magnitude of the vector
difference between successive normalized gradients equal to 0.01. When the ES1 method
is used with these choices for the stabilization step size and the tolerance in the allowed
magnitude of the vector difference between successive normalized gradients, the
algorithm is called the optimized ES1 method or ES1*.
The program also allows one to use the Page-McIver algorithm [Ref. 17, Sect. 22], rather
than the ESD or Euler stabilization method, to compute the reaction path. In our
implementation of the Page-McIver method, the first step away from the saddle point is
again taken as described above, and subsequent steps are taken using a local quadratic
approximation (LQA) as described in [Ref. 17, Sect. 22] or in the hard-copy manual for
version 1.5.
Polyrate can also use the variational reaction path algorithm based on the Euler steepest-
descents method, called VRP(ESD) [Ref. 49, Sect. 21], to construct the reaction path.
Methods for calculating the reaction path are discussed further in Sect. 10.D.
Polyrate 43
In order to obtain the partition functions needed to evaluate kGT(T, s), a generalized
normal mode analysis is performed at regular intervals along the reaction path. This is
done at the points referred to as the save grid. The generalized normal mode analysis
can be carried out in either rectilinear (Cartesian) or curvilinear coordinates. (It is very
important to use curvilinear coordinates rather than Cartesian coordinates for VTST
calculations; Cartesian coordinate will very likely yield imaginary frequencies along the
reaction coordinate, which will cause unphysical VTST results.)
The algorithm used for rectilinear coordinate calculations is discussed by Miller, Handy,
and Adams [Ref. 7, Sect. 22]. In particular, for s 0 the rectilinear or Cartesian
generalized normal modes orthogonal to the reaction path are obtained from the projected
force constant matrix
FP s( ) = 1-P s( )[ ]F s( ) 1-P s( )[ ] , (3)
where F(s) is the full (3N 3N) Cartesian force constant matrix evaluated at a point on
the MEP, and [1 - P(s)] is a projector used to project the direction along the reaction path
as well as overall rotations and translations out of the space associated with the non zero
eigenvalues. Diagonalization of FP(s) gives 7 zero and 3N–7 positive eigenvalues (6 zero
and 3N–6 positive eigenvalues for linear molecules, or 1 zero and 3N–1 positive
eigenvalues for adsorbed species) corresponding to the bound generalized normal modes
orthogonal to the reaction coordinate. After the frequencies are calculated, the
frequencies and corresponding eigenvectors are placed in canonical order (which is
defined in Section 6.E). If the REORDER keyword is specified, the code will attempt to
correlate the modes from point to point in terms of their physical characters rather than
their magnitudes. Thus the first mode would be the mode with the highest overlap with
the first mode at the previous point, rather than the highest-frequency mode, and so forth.
The REORDER option would be useful for studying diabatic correlations of vibrational
modes. Once the frequencies have been reordered anharmonicity corrections, the zero
point energy, and the ground-state adiabatic energy are computed as they were at the
saddle point.
The curvilinear generalized normal mode analysis is carried out by first transforming the
Cartesian force constant matrix into a curvilinear coordinate system, then projecting out
the gradient components, and finally diagonalizing the projected curvilinear force
Polyrate 44
constant matrix according to Wilson GF method [Refs. 36 and 37 of Sect. 22] as
described in Refs. 41, 43, 45, and 46 of Sect. 21. Generalized normal mode frequencies,
the zero point energy, and the ground-state adiabatic energy are then computed as they
were at the saddle point. Methods for calculating the curvilinear generalized normal
mode frequencies are discussed further in Sect. 10.M.
Section 10 and the GTST book chapter give details of the WKB method for computing
anharmonic vibrational energies.
Starting with Polyrate version 4.0, vibrational modes corresponding to torsional motion
can be treated with the hindered-internal-rotator approximation [Refs. 24, 29, and 34,
Sect. 21].
6.G.2. NOSADDLE option
The NOSADDLE option is used only for strictly downhill association reactions. It requires
the user to input an initial guess for a point on the MEP such that the variational
transition state lies between this point and the product, which is the associated molecule.
Let s = 0 denote the initial guess, and let
sP denote the value of s at the product.
Typically, one will compute the MEP only up to some value
s2 that is less than
sP.
Furthermore, the first few points are typically not useful because it takes a few steps for
the path generated by the steepest descent algorithm to become sufficiently close to the
MEP. If this occurs by
s = s1, where
0 £ s1 £ s2, then it is the user’s responsibility to
ensure that the variational transition state lies between
s1 and
s2.
Starting with Polyrate version 2008, VRC option is recommended instead of NOSADDLE
option for barrierless association reactions. The VRC option uses a variable reaction
coordinate and single-faceted or multifaceted dividing surfaces. See Sections 11 and 13
for details.
6.H. Reaction-path curvature
The curvature of the reaction path is used in both the SCT and LCT calculations. The
curvature of the reaction path is a vector with F – 1 components, where F is the number
of internal degrees of freedom (F = 3N – 6 for a gas-phase reaction with a nonlinear
Polyrate 45
reaction path, F = 3N – 5 for a gas-phase reaction with a linear reaction path, and F = 3N
for a solid-state reaction employing a fixed lattice, as in the embedded-cluster method).
In this manual the components of the curvature vector are denoted BmF, m = 1,2, ...,F-1,
where m labels a generalized-normal-mode direction.
When using an analytic potential energy surface or electronic structure input data from
unit fu30 or unit fu40, there are three choices for how to compute BmF. The first two
choices are based on eq. (98) of the GTST book chapter [Ref. 5, Sect. 21]. This formula
involves a numerical derivative of the negative gradient, and this derivative may be
computed by central or one-sided finite differences. The third choice is to use eq. (48) of
a paper by Page and McIver [Ref. 17, Sect. 22]. Notice that eq. (98) of the GTST book
chapter is the same as eq. (47) of Page and McIver paper. An advantage of eq. (48) is
that it does not involve numerical differentiation of the gradient. Both formulas require
the generalized-normal-mode eigenvectors so the curvature is calculated on the Hessian
grid (as opposed to the gradient grid). The evaluation of the curvature by taking the
derivative of a quadratic fit to the gradient at three points (i.e., a central finite difference)
is specified by the option dgrad of the keyword CURV; the evaluation by taking the
derivative of a one-sided two-point fit to the gradient is called oneside, and the
evaluation by eq. (48) of Page and McIver is called dhess because it involves a
derivative of the Hessian. Although in principle, dhess can be used even when the
reaction path is calculated by the ESD method, this can be dangerous because the
accuracy of a numerical derivative requires a small step size. When the ESD method is
used to calculate the reaction path, the gradient may be known on a much finer grid than
the Hessian grid, and numerical differentiation of the Hessian may be inaccurate. If the
dhess option is used with an ESD integration scheme, one should be especially careful
to converge the Hessian with respect to INH.
These methods all break down (become unstable) at or very near to the saddle point.
Thus the code does not obtain the curvature vector directly at the saddle point. Instead it
obtains the value of BmF at the saddle point by linear interpolation of the absolute values
at the closest negative-s save grid point and the closest positive-s save grid point. That is,
if the saddle point is sNS , one obtains the curvature at the saddle point as an average of
the values at
sNS-1 and
sNS+1 if INTMU equals 1, and one obtains the curvature at the
saddle point as an average of the values at
sNS-2 and
sNS+2 if INTMU equals 3. The
curvature at the saddle point is used to calculate
meff (s) at sNS . There is an option to
compute
meff (s) at
sNS,
sNS-1, and
sNS+1 by linear interpolation of the values at
sNS-2
Polyrate 46
and
sNS+2. This option is corresponds to setting INTMU equal to 3 in the PATH section,
this is currently the default.
When using the electronic structure data from unit fu31, the method for computing BmF
is automatically chosen based on whether or not a gradient is available at the closest point
on both sides of the Hessian point. If gradients are available on both sides of the point
then the three gradients are fit to a quadratic function and the derivative of this function is
calculated and then evaluated at the Hessian grid point. If the gradient is only available
on one side then the derivative is evaluated by one-sided difference. For obtaining the
curvature vector at the saddle point the procedure described above is also used.
However, if the user selects to perform a direct interpolation of the exponent in eq. 10 of
Ref. 48 in Sect. 21, the IVTST-M calculation will obtain eff at the saddle point from a
spline fitting of the exponent as a function of the mapping variable z. See Section 6.N.2
for more IVTST-M details.
In contrast, when data is obtained from unit fu29, which is used for IVTST-1
calculations, the curvature at the saddle point is computed using an alternative formula
presented as equation (49) in the Page and McIver article [Ref. 17 of Sect. 22], and its
value at the "extra point" is computed again using eq. (48) of the same reference. The
value at the saddle point is actually used in the IVTST-1 calculation, whereas the value at
the extra point is computed for informational purposes only.
See Section 10.F for further discussion of the curvature calculations.
6.I. Transmission coefficients
The temperature-dependent ground-state transmission coefficient is the ratio of the
Boltzmann average of the quantum energy-dependent ground-state transmission
probability to the Boltzmann average of the energy-dependent transmission probability
corresponding to classical-reaction-coordinate motion with other degrees of freedom in
the ground state. Both transmission probabilities are zero for an energy lower than the
maximum of the ground-state energy of the reactants and of the products. For VT, the
threshold energy for the classical transmission probability is the maximum of the
adiabatic ground-state energy
VaG s( ) , i.e.,
VaAG ; it is
VaG s = 0( ) for TST and
VaG s = s*
CVT( ) for CVT. One can factor the ground-state transmission coefficient into
Polyrate 47
two factors. The first factor is a ratio of the Boltzmann average of the quantum
transmission probability to the Boltzmann average of the classical transmission
probability with the threshold energy at the maximum of the adiabatic ground-state
energy. The second factor is a ratio of the Boltzmann average of the classical
transmission probability with the threshold energy at the maximum of the adiabatic
ground-state energy to the Boltzmann average of the classical transmission probability
with the threshold at the value that is consistent with the level of variational theory being
applied. In the FORTRAN unit fu6 output, the first factor is denoted as ZCT, SCT,
LCG3, LCG4 and the second factor is denoted as TST/CAG and CVT/CAG for the TST
and CVT levels of theory, respectively. Since this CAG factor is exactly 1 in the case of
VT, it is not listed in the output. The final result is denoted as, e.g., CVT/ZCT for a
transmission coefficient evaluated with the ZCT (or MEPSAG) method at the CVT level.
The CAG factor is required for consistency in TST and CVT calculations (but not in VT
calculations), although it is often close to unity. The CAG correction was introduced in
Refs. 10 and 44 of Sect. 22, and the reader is referred to those references for further
discussion.
The MEPSAG, CD-SCSAG, and LCG3 or LCG4 transmission coefficients are simply
denoted ZCT, SCT, and LCT, respectively, in recent papers, as discussed in Section 6.D
above. The ZCT method should be considered simply as an approximation to SCT to be
used when insufficient information is available to compute the reaction-path curvature.
The SCT transmission coefficient is always larger than (or equal to) the ZCT one. The
SCT transmission coefficient is expected to be larger than and more accurate than the
LCT one when reaction-path curvature is small over the classically forbidden segment of
the reaction path; the LCT transmission coefficient is expected to be larger than and more
accurate than the SCT one when reaction-path curvature is large in the classically
forbidden section of the VaG(s) curve. These two situations are discussed in more detail
in discussion remarks at Faraday Symposium 29 on Potential Energy Surfaces and
Organic Reaction Paths [Ref. 45 in Sect. 22], and they are illustrated (in color) in an
earlier review article [Ref. 46 in Sect. 22].
Whenever there is enough information available to calculate LCT transmission
coefficients there is also enough data available to calculate SCT ones (although the
converse is not true). In such cases the recommended best estimate is obtained by the
Polyrate 48
microcanonical optimized multidimensional tunneling (µOMT) approximation that is
discussed in Section 6.M.2 below.
The optimized multidimensional tunneling approximations are reviewed below. In
particular, Subsection 6.M.1 reviews the canonical optimized multidimensional tunneling
(COMT) method, and Subsection 6.M.2 discusses the microcanonical optimized
multidimensional tunneling method (µOMT).
6.J. Reaction rates including tunneling
In this subsection, we describe the calculation of the reaction rate constants as discussed
in Subsection 6.A.
For a given temperature T, various transmission coefficients (T) are computed using
methods selected by the user, all of which lead to different approximations to the rates.
Next, the s-independent quantities are determined, i.e., the electronic, translational,
rotational, and vibrational partition functions for reactant(s) and product(s), as well as the
electronic partition function for the generalized transition state and the prefactor for the
rate constant.
Next, for each s at which a generalized normal mode analysis was performed the program
computes the rotational and vibrational partition functions of the generalized transition
state to get the generalized free energy of activation at this value of s. Using the nearest
points to the maximum, parabolic and quartic fits are used to obtain the interpolated
maximum of . The final location and generalized free energy of activation
at this maximum are obtained from the quartic fit (the parabolic fit is just for
comparison).
The calculation of the kappa factors is described next. The Wigner tunneling correction
for conventional TST is also computed, but only for informational purposes. It is not a
recommended method because it is just the first two terms in a slowly convergent or
divergent series. For thermal reaction rates, the MEPSAG, CD-SCSAG, and LCG3 or
LCG4 transmission probabilities are averaged over a thermal distribution and divided by
the thermal average of the classical transmission probabilities. As mentioned previously,
CD-SCSAG, LCG3, and LCG4 methods take into account the coupling between the
Polyrate 49
reaction path curvature and the vibrational modes. In this version of POLYRATE, the
LCG3, LCG4, and CD-SCSAG methods treat vibrational modes harmonically. (The
current version of the program will not perform LCG3 or LCG4 calculations if
anharmonic options other than the hindered-rotator method are selected. In the case of
CD-SCSAG, zero-point energies and vibrational partition functions can be treated using
one of the various anharmonicity methods, and the CD-SCSAG kappa factor will change
due to the change in the adiabatic ground state potential. However, the CD-SCSAG
method is still based on a harmonic approximation.) The procedures for calculating the
transmission probabilities and transmission coefficients for the MEPSAG method are
described completely in the GTST book chapter, and the description of the CD-SCSAG
method can be found in Refs. 29 and 31 of Sect. 21. For the LCG3 or LCG4 calculation
the basic idea is in the GTST book chapter and additional details of the implementation
are described in Refs. 21, 29, 31, and 34 of Sect. 21. (Note that the value of s along an
LCG3 or LCG4 tunneling path is a continuous function of progress along the path, as
described correctly in the GTST book chapter and not as described in Ref. 21 of Sect.
21.)
Early versions of Polyrate used a method called SCSAG. This has now been replaced by
CD-SCSAG. The two methods are identical if the reaction-path curvature has only one
nonzero component; otherwise they differ, and CD-SCSAG is based on a more correct
analysis of the geometry of corner-cutting tunneling.
In the Polyrate program, the Kronrod quadrature for MEPSAG and CD-SCSAG
tunneling calculations is performed using the independent variable s and abscissa gi
rather than y and yi; see page 99 of the GTST book chapter.
Furthermore, for both the (E) integral over s, eq. (94), and the Boltzmann average, eq.
(91) of the GTST book chapter, the range of integration is divided into 1-3 equal
segments, and the same order of Kronrod quadrature is used in each. For the (E)
integral we use NSEG2 segments with (2*NQTH+1)-point Kronrod quadrature in each, and
for the Boltzmann integral we use NSEG segments with (2*NQE+1)-point Kronrod
quadrature in each. Kronrod's method provides NQTH-point and NQE-point Gauss-
Legendre quadrature results as well. It is important to check the convergence of these
integrals by comparing the N-point and (2N+1)-point results.
Polyrate 50
The CD-SCSAG and LCG3 or LCG4 transmission probabilities are also used to calculate
optimized multidimensional tunneling approximations called COMT and OMT, as
discussed in Sections 6.M.1 and 6.M.2.
Using the various generalized transition state approximations and k (T) factors, various
forward and reverse rate constants at temperature T can be obtained, e.g., the combination
of an CVT rate constant with an MEPSAG tunneling correction yields an CVT/MEPSAG
rate constant.
If the VTST-IOC correction is selected, the program updates all the energy, frequency,
and determinant of moment of inertia information to the corrected values and recalculates
the tunneling probabilities. A new set of corrected rate constants is then obtained.
If the VTST-ISPE correction is selected, the program spline fits the differences of the
lower-level energies and the higher-level energies using the IVTST-M algorithm. The
interpolated values are then added on to the lower-level and a new set of corrected rate
constants is obtained. See Section 10.J for a detailed description.
6.K. Imaginary-frequency modes transverse to the reaction path
When a generalized normal mode eigenvalue is negative, i.e., the harmonic frequency of
a mode transverse to the reaction path is imaginary (recall that the eigenvalues are
squares of the frequencies), the program takes the following actions:
1. When an independent-normal mode method is being used, the vibrational
partition function of that mode is set equal to 1.0 1010.
2. The zero-point energy of that mode, as required for the calculation of the
vibrationally adiabatic ground-state potential curve for tunneling calculations,
is set equal to zero.
3. The turning point distance of that mode is set equal to 1.0 1010 bohr for the
LCG3 or LCG4 calculations.
4. For the CD-SCSAG method, no contribution from this mode is included
whether the harmonic or anharmonic approximation is selected.
Polyrate 51
6.L. Equilibrium constant calculation
In the current version of the code this calculation is the last to be performed. However,
the calculation is carried out in two different subroutines, TSOUT and FINOUT. If a TST-
only calculation is requested, then all the rate calculations are carried out in the
subprogram TSRATE, which calls TSOUT. TSOUT prints the rate constants to the fu6 file
and the fu15 (summary) file, and it calculates and prints the equilibrium constants using
the TST rate constants.
The subprogram RATE, which calls FINOUT, calculates the rate constants with canonical
variational theory (CVT). FINOUT computes and prints final rate constants, activation
energies, and equilibrium constants (from the CVT rate constants).
In both cases the equilibrium constants are the last quantities calculated in the respective
subprograms.
6.M. Omitting the product
Polyrate can be run without calculations on the product if reverse rate constants
and equilibrium constants are not calculated. This requires specifying the FORWARDK
keyword in the RATE section of the fu5 input.
What the code will do then depends on whether there is a WELLP section in the
fu5 input. If there is a WELLP section, the interpolation extends to the product-side well
as described at Section 3.1 of Ref. 48 of Sect. 21. If there is not a WELLP section, then
the interpolation extends to the last nonstationary point on the product side. Thus
VMEP(s) is cut off (down to the product value) at that point, and if tunneling extends into
the region beyond the last nonstationary point on the product side, it will be
overestimated.
Polyrate 52
6.N. Optimized multidimensional tunneling calculations
6.N.1. COMT method
The canonical optimized multidimensional tunneling (COMT) temperature-dependent
transmission coefficient is the larger of the thermally averaged temperature-dependent
transmission coefficients calculated by the CD-SCSAG method and the LCG3 or LCG4
method at a given temperature. The COMT method was first used in Ref. 28 of Sect. 21
(where it was simply called MT). It was first called COMT in Ref. 34 of Sect. 21.
6.N.2. µOMT method
The microcanonical optimized multidimensional tunneling (µOMT) temperature-
dependent transmission coefficient is the ratio of the Boltzmann average of the µOMT
quantum transmission probability to the Boltzmann average of the classical transmission
probability, where the µOMT quantum transmission probability is the larger of the
energy-dependent transmission probabilities evaluated by the CD-SCSAG method and
the LCG3 or LCG4 method at a given energy. This method was introduced in Ref. 34 of
Sect. 21. See Also Ref. 45 in Sect. 22.
6.O. Interpolated VTST and mapped interpolation
Calculating
VMEP(s), |I(s)|, and
w(s) as needed for variational transition-state theory
and tunneling calculations from ab initio electronic structure theory can be
computationally demanding. Thus, it is sometimes desirable to interpolate these
quantities based on electronic structure data only at the reactant, product, saddle point,
and optionally a small number of additional points (close to the saddle point) along the
MEP. Variational transition-state theory based on interpolated data at a few points on the
MEP [Ref. 43 in Sect. 22 and Refs. 26, 32, and 48 in Sect. 21] is called interpolated
VTST or IVTST.
Three implementations of IVTST are included in this version of the Polyrate program.
The first is zero-order IVTST (IVTST-0) and the second is first-order IVTST (IVTST-1)
using the global interpolation approach. The third is IVTST-M which is described in
Section 6.O.2 and 6.O.3. Permutation of frequencies is not included in any of these
Polyrate 53
methods. TST rates and ZCT transmission coefficients can be calculated with IVTST-0;
in addition CVT rates and SCT transmission coefficients can be calculated with IVTST-
1. Moreover, IVTST-M may be used for TST, CVT, VT, and CUS rates and ZCT and
SCT transmission coefficient calculations.
6.O.1. IVTST-0 and IVTST-1
IVTST-0 and IVTST-1 calculations [Ref. 26, Sect. 21] can be performed for bimolecular
reactions by using the IVTST0 or IVTST1 keywords in the GENERAL section. Alternatively,
IVTST-0 calculations can be performed using file fu50. Presently IVTST-0 and IVTST-
1 methods are only available for bimolecular reactions with two reactants and two
products.
The IVTST-0 method assumes that information is only available at three locations on the
potential energy surface, namely at the reactant (R), saddle point, and product (P).
Details of the interpolation procedures can be found in Ref. 26 of Sect. 21. The IVTST-0
rate constant is the conventional TST rate constant with ZCT tunneling. Note that ZCT
tunneling is the only available tunneling method for IVTST-0. ZCT tunneling
calculations for zero-order IVTST are carried out using
VaG (s) = VMEP + ZPE(s),
where
VMEP(s) is represented by an Eckart function and ZPE(s) is obtained from
interpolated values.
The IVTST-1 method requires information for one extra point (
s = s1) near the saddle
point in addition to the saddle point, R, and P. The
VMEP(s) curve for the IVTST-1
calculation is also approximated by an Eckart function with a constraint that the Eckart
function goes through the extra point at
s = s1. To determine the location of the
variational transition state, the forward standard-state free energy of activation profile,
is calculated using the interpolated
VMEP(s),
I(s) , and
w(s). The SCT
transmission coefficients can be obtained for first-order IVTST using the interpolated
meff (s).
IVTST-0 calculations can also be performed by using the keyword ICOPT in the GENERAL
section and the keyword 0IVTST in the unit fu50 input (see Subsection 12.F). In the
current version, this method is available only for bimolecular reactions with two
Polyrate 54
products, and therefore the keywords MEPTYPER and MEPTYPEP for the unit fu50 input
should both be set to 2. In addition, the keywords MEPTYPER and MEPTYPEP should not be
set to well, and the keyword FREQMAT should not be used. The hindered rotor
approximation is currently the only anharmonicity option that can be used with IVTST-0
when using file unit fu50 for the IVTST-0 calculation. At this time there are no
anharmonicity options for IVTST-0 nor IVTST-1 calculations when using file unit fu29.
For the IVTST-0 calculations, only conventional transition state theory rate constants and
ZCT transmission coefficients can be calculated. Variational transition state theory at the
CVT level and both ZCT and small-curvature tunneling (SCT) transmission coefficients
can be obtained for IVTST-1. Details can be found in Ref. 26 of Sect. 21.
6.O.2. Interpolated VTST by mapping (IVTST-M)
IVTST-M is a method for obtaining the information required for a VTST calculation all
along the reaction-path from the information available at a small number of points. The
only limitations on using the IVTST-M algorithm are that a saddle point exists and
reaction path information is available for least one nonstationary point on each side of the
saddle point. In addition, as in all IVTST methods, information is required for 3 – 5
stationary points (reactants, saddle point, products, and optionally one or two wells). The
level of IVTST-M is denoted by two numbers, H and G, indicating respectively the
number of nonstationary points at which Hessians are available and the number of
nonstationary points at which gradients are available. Thus, IVTST-M-6/54 indicates that
the interpolation is based in 6 nonstationary Hessian points, at which geometries,
energies, gradients, and Hessians are available, and 48 points (which is 54 minus 6) for
which only geometries, energies, and gradients are available. The mapping procedure
transforms VMEP(s), |I|(s), (s), and Bm,F(s) from functions of s into functions of z where
z is a new variable which always has a finite value, whereas s can have infinite values if
either forward or reverse reaction is bimolecular. The parameter z is determined as
z = 2p
arctans - s0
L
æ
è ç
ö
ø ÷ , (1)
with s0 and L being two parameters obtained from the forward and reverse barrier heights
[Ref. 48 in Sect. 21].
Polyrate 55
The new VMEP(z), |I|(z), (z), and Bm,F(z) functions are interpolated by using splines
under tension.
The method employs different approaches for the interpolation of VMEP(s), depending on
the number of reactants and products in the reaction. If the reaction is unimolecular in
either the forward or reverse direction, a cubic polynomial for estimating 10 energies
between the reactant (or product) and the first (or last) point on the reaction path (or
between the reactant and the first point and between the product and the last point) is
calculated before carrying out the spline under tension fit. The cubic polynomial can be
function of either s or z. The user should base the choice of s or z on experience or should
test the two choices (using function of s or z) to see which one gives reasonable potential
energy curve. The user can also choose not to use the polynomial to generate the 10 extra
energies; however, the default is to generate them by using a cubic polynomial function
of z. If the forward reaction is bimolecular, the interpolation on the reactant side of the
saddle point is based on the energies from the input plus 10 additional energies estimated
from an Eckart polynomial with a range parameter which is a function of s. Similar
considerations apply on the product side if there are two products.
If for a bimolecular reaction or a reaction with two products, there are wells on the
reactant and/or product side, the interpolation can be done using the information on these
stationary points with the unimolecular procedures, which at least in principle can make
the interpolation more accurate, especially when the well is deep and/or close to the
saddle point. But if a well is present, it can also be ignored, and the interpolation can be
carried out using reactants and/or products. If the well is ignored, then since for
bimolecular reactions (or bimolecular sides of the reaction path) the interpolation is based
on an Eckart potential, no point on the reactant side of the reaction path can be used that
has an energy lower than the reactants energy, and no point on the product side can be
used that is more stable than the products.
The IVTST-M algorithm has been implemented to be used with the hooks and the
electronic structure input files, unit fu30, fu31, and fu40. The method is fully operational
when using the hooks and the unit fu31 input file. When using units fu30 and fu40, only
the IVTST-M default options are available. To use the IVTST-M algorithm with unit
fu30, LOPT(2) must be set equal to –1; and with fu40, MAXLPTS must be set equal to –1.
Polyrate 56
Whenever IVTST-M calls TSPACK for a spline-under-tension fit, it sets the variable
IENDL equal to 3. This means that the two extra pieces of data needed for the spline fit
are generated by the ENDSLP subroutine using a local spline under tension.
6.O.3. The mapped interpolation (MI) algorithm with the hooks
As mentioned in Section 1 of this manual, the mapped interpolation (MI) algorithm can
be used in two ways by POLYRATE. The first way is to perform IVTST-M calculations
using electronic structure input file fu30, fu40, or fu31. This method is described fully in
Sections 6.N.2, 10.J, and 11.D of this manual. The second way is in conjunction with the
hooks; this requires some additional comments, which are given in the rest of this section.
A calculation with the hooks involves two stages. At the end of the first stage, one has
stored s, VMEP(s), and the gradients on the fine grid and s, VMEP(s), (s), BmF (s), and
( )I s are stored on the save grid. (The grids are defined in Sect. 7.A) Both grids extend
from s = SLM on the reactant side to s = SLP on the product side, and there are G + 1
points (including the saddle point but excluding reactants and products) on the fine grid
and H + 1 points (including the saddle point but excluding reactants and products) on the
save grid. Then mapped interpolation is carried out to add EXNSTEP * EXSTEP points on
each side of the grids. Furthermore SLM is replaced by SLM – EXNSTEP * EXSTEP, and SLP
is replaced by SLP + EXNSTEP * EXSTEP. As should be clear from Section 12.A.7,
EXNSTEP and EXSTEP may actually be different on the two sides.
6.P. Interpolated optimized corrections (VTST-IOC), a form of dual-level VTST
In VTST calculations with approximate potential energy surfaces, it is sometimes
desirable to correct the classical energies, vibrational frequencies, and moment-of-inertia
determinants of some points along the MEP (e.g., the reactant, saddle point, product, van
der Waals complex, ion-molecule complex, etc.) with accurate (higher-level) results. This
is accomplished by applying correction procedures to the calculated energy, frequencies,
and moment-of-inertia determinant along the MEP. The corrections are calibrated such
that the corrected results match the accurate values at those selected points, and they
correspond to interpolating these corrections at other points. When the corrections
involve data from higher-level optimizations of the stationary points, the method is called
Polyrate 57
VTST-IOC, a special case of VTST-IC. The original correction procedure for
frequencies is denoted ICA, and two improved procedures are denoted ICR and ICL. (In
general we recommend the ICL procedure.) The ICA procedure was introduced in
version 5.1 of POLYRATE, and the ICL and ICR procedures were introduced in version 7.0.
All three procedures are based on the correction at 3 points, in particular, the saddle point
and two stationary points, one on each side of MEP.
There are also two procedures for correcting VMEP(s) in IOC calculations: the original
method, which was called NOECKART in versions 7.2 – 7.9.2 of Polyrate but now is called
the single-Eckart (SECKART) method of interpolating VMEP, and the newer method, which
was called ECKART in versions 7.2 – 7.9.2 but now is called double-Eckart (DECKART).
The ECKART option was introduced in version 7.2. As implied by the names of the
correction, is either a single Eckart function or a difference of two Eckart terms. If there
is an appreciable well on either side of MEP, it is recommended that one use the
molecular complex corresponding to the well as the stationary point on that side of the
saddle point; otherwise it is recommended that one use the reactant or the product.
However, if the well on the MEP is not very deep or if accurate data for the complex
corresponding to the well are not available, the user can neglect the well and choose an
appropriate functional form for the correction function as if there were no well at all.
As discussed in Section 1, the VTST-IOC method can be used either with an analytic
potential energy surface or with electronic structure input data for the lower-level surface.
In either case, the information calculated from the potential energy surface or read from
the electronic structure input file will be corrected by the higher-level values.
The functional forms we use for the correction functions are an Eckart function, a
hyperbolic tangent, a cut-off Gaussian, or a cut-off hyperbolic tangent, depending on the
shape of MEP under consideration and the relative correction values at the 3 stationary
points. See Refs. 36 and 44 of Sect. 21 for details. Details for the ICA procedure are
available in Subsection 10.H and in Ref. 36 of Sect. 21 and details for the ICR and ICL
procedures are available in Subsection 10.H and in Ref. 44 of Sect. 21. Details of the
double Eckart procedure are available in Ref. 44 of Sect. 21.
If the higher-level data is obtained at electronic structure level X, and the lower-level data
is obtained at level Y, the VTST-IOC calculation may be denoted X///Y. The triple slash
notation is similar to the double slash notation that is widely used in electronic structure
Polyrate 58
calculations. In particular, // means “at a stationary point geometry optimized by...”
whereas /// is loosely translated as “along a reaction path calculated by...”. More
specifically, though, we reserve the IOC and triple slash notations for algorithms were the
higher-level information supplied to “correct” the transition state data involves a higher-
level geometry optimization. If only single-point energies are used, the ISPE and double
slash notation should be used.
6.Q. Interpolated algorithm for large-curvature tunneling calculations
In LCT calculations, for each energy, a tunneling path is defined as a straight line in
isoinertial coordinates between two reaction-coordinate turning points lying on the MEP,
on the reactant side and on the product side of the maximum of the vibrationally adiabatic
potential. This straight-line is divided into three zones, two of them are in the reactant
and product valleys, respectively, and they are vibrationally adiabatic, and another zone
describes the middle zone of the straight-line path and is vibrationally nonadiabatic. In
the interpolated LCT (or ILCT) algorithm, every time the potential energy is needed
along the nonadiabatic segment of the tunneling path, this energy is calculated by means
of the spline fit to a number of already calculated points. Details of the methods are
available in Ref. 55 of Sect. 21.
Polyrate 59
7. PROGRAM STRUCTURE
7.A. Overview of program flow
As mentioned in the Introduction, the Polyrate program has several possible ways to
obtain the reaction-path information necessary for rate constant calculations. The first
option is to calculate this information directly from a set of interface subprograms called
hooks. The second is to read this information from an electronic structure input file
(fu30, fu31, or fu40) consisting of geometries, gradients, Hessians, etc. at points on the
MEP obtained from electronic structure calculations. The third option is to read the
information from a restart file which has been saved from a previous Polyrate run. The
fourth option is to read in higher-level “corrections” at selected points along the MEP;
these corrections are read from file fu50 for VTST-IOC and from file fu51 for VTST-
ISPE. Finally, for the IVTST calculations, electronic structure data at selected points
may be read from file fu29 (IVTST-0 and IVTST-1) or fu50 (IVTST-0). These options
are implemented in the Polyrate program as follows.
First, the MAIN program reads all the keyword input. These keywords are analyzed for
possible conflicts (i.e., unsupported combinations of options) in subroutine OPTION. If it
is a restart run then the program reads in the restart information in RESTOR, and the rate
constant calculation proceeds as described in the last paragraph of this section.
Otherwise, all other input data from unit fu5 are read in and checked by READ5 and
REDGEO.
The GENERAL section of keyword input (Section 12.A.2) is always read first. Depending
on the options chosen the properties of the reactants, products, and generalized transition
states are calculated by calls to the hooks or read in from an electronic structure input file
(or both). The user can choose at most one of the two switch keywords IVTST0 and
IVTST1, or use the DL keyword. This choice plus the choice made for the POTENTIAL
keyword in the ENERGETICS section (Section 12.A.3) determines the basic outline of the
rest of the calculations as indicated in the following table. That table assumes that the
hooks call SURF and SETUP, which is the standard way to use the hooks when Polyrate is
used as a stand-alone code. (Subprograms SURF and SETUP are described in Subsection
8.C, and a more complete description of the hooks is provided in the rest of Section 8).
In the present version of the code, user can also turn on the VRC option, which is off by
default, to calculate rate for barrierless association reactions using a variable reaction
coordinate and multifaceted dividing surfaces. When VRC is turned on, potential energies
Polyrate 60
can only be calculated through hooks since the Monte Carlo method is used for the
variable-reaction-coordinate calculations with single-faceted or multifaceted dividing
surfaces. Gradient and Hessian are not required for all Monte Carlo samples.
Polyrate 61
DL IVTST0 IVTST1 POTENTIAL Action
None off Off hooks Single-level calculation
based on whole reaction
path calculated from an
analytic PES.
none off Off unit30, unit31, or unit40
Single-level direct
dynamics based on
whole reaction path
calculated from an
electronic structure input
file on unit fu30, fu31, or
fu40
none on Off unit29 or unit50
Single-level direct
dynamics IVTST-0
calculation based on
electronic structure input
data from unit fu29 or
fu50
none off On unit29 Single-level direct
dynamics IVTST-1
calculation based on
electronic structure input
data from unit fu29.
ic off Off hooks Dual-level direct
dynamics with lower-
level data from analytic
PES and higher-level
data from unit fu50
ic off Off unit30, unit31, or unit40
Dual-level direct
dynamics with lower-
level data from unit
fu30, fu31, or fu40 and
higher-level data from
unit fu50
ispe off Off hooks Dual-level direct
dynamics with lower-
level data from analytic
PES and higher-level
data from unit fu51
ispe off Off unit30, unit31, or unit40
Dual-level direct
dynamics with lower-
level data from unit
fu30, fu31, or fu40 and
higher-level data from
unit fu51
Polyrate 62
In the analytic potential energy surface case, the equilibrium geometries and properties of
the reactant and product species are optionally obtained in subroutine REACT. For
polyatomic species, REACT calls POLYAT, and the user must supply an estimate of the
equilibrium geometry. POLYAT calls NEWT to perform a Newton-Raphson search for the
location where the first derivatives of V are zero, CENTER to place the origin at this
location and evaluate the determinant of the moment of inertia tensor, and NORMOD to do
a vibrational analysis. The vibrational analysis involves determining the normal mode
eigenvectors and frequencies, and, if desired, one of several procedures for including
anharmonicity is invoked in ANHARM. If a diatomic species is treated as a Morse
oscillator (DIATOM keyword) REACT calls DIATOM, and the equilibrium geometry,
dissociation energy, and range parameter must be supplied by the user.
Next, if using he RP-VTST option without NOSADDLE, the program will determine the
saddle point geometry and properties for the tight transition state. This is done in SADDLE
and MAIN, which in turn call the same subroutines used by POLYAT. The program will
handle 0 or 1 saddle points. For one saddle point the user must supply an approximate
geometry for its location. For 0 saddle point, user can choose NOSADDLE option, which
requires the user to input an initial guess for a point on the MEP such that the variational
transition state lies between this point and the product. However, rather than using
NOSADDLE, the VRC option in GENERAL section is recommended for barrierless
association reactions, and this option does not require to input any geometry for transition
state.
When using the hooks, Polyrate starts either at the saddle point just determined or from
an input starting-point geometry, then computes the minimum energy path (MEP) by a
choice of several methods (done in the PATH section of file fu5). The distance along the
MEP is called s; the user can make s be zero at the saddle point, negative in the reactant
region, and positive in the product region. The initial step can be based on a cubic
expansion of the potential energy surface determined from the normalized eigenvector of
the imaginary-frequency normal mode and from the curvature vector, both of which are
calculated at the saddle point, or the initial step may be taken along the normal coordinate
for the unbound motion at the starting point. When the default ESD method is used (RPM
keyword set equal to esd), the negative of the gradient in isoinertial coordinates is
followed using a fixed gradient step size DEL (specified by the SSTEP keyword). At
regular intervals (specified by the INH keyword) along the MEP, the program computes
Polyrate 63
the generalized-transition-state properties necessary to evaluate the generalized free
energy of activation and to perform semiclassical tunneling corrections. (We emphasize
that both DEL and the regular intervals are measured in the isoinertial coordinates. Thus
the units are sometimes called mass-scaled angstroms instead of angstroms. Thus if
REDM, specified by the SCALEMASS keyword which is described in Subsection 12.A, is
changed, DEL and the regular intervals will have different meanings.) Note that the grid
determined by DEL is called the fine grid or the gradient grid. The grid defined by the INH
keyword is called the save grid or Hessian grid. This is discussed further in Subsection
10.D. The moment of inertia calculation and Miller-Handy-Adams projections (eq. 31 of
Ref. 5) or curvilinear-reaction-coordinate projections (eq. 17 of Ref. 41) are carried out in
PROJCT; the vibrational analysis and the calculation of the effective mass for tunneling are
done in NORMOD. In addition, if there is a saddle point the mapped interpolation (MI)
algorithm can be used to interpolate the energy, the frequencies, the determinant of the
moment of the inertia tensor, and the curvature components to extend one or both ends of
the MEP for tunneling calculations. (See Sections 6.N.3 and 8.A for more details.)
When there is no saddle point a simple exponential extrapolation of the classical and
adiabatic energies and the other quantities used for tunneling calculations can be used at
one or both ends of the MEP. (See Sect. 10.A for more details.) The EXFIRST and
EXSECOND keywords in the PATH section control interpolation (extrapolation) options.
Interpolation (extrapolation) is especially useful in situations where a minimum is
reached in the classical potential before the adiabatic barrier is low enough for computing
converged tunneling probabilities. Notice that extending the grid is sometimes called
extrapolation, but it is also called interpolation because one used the reactant or product
information that technically it is indeed interpolation.
When the MEP calculation is completed, the reaction-path information can be saved by
writing it to unit fu1 for later restart runs. We note that there is an upper limit of NSDM
points at which the reaction path information can be saved in a given Polyrate executable
file. The parameter NSDM is defined in the file aamod.f90 (see Subsection 5.A.2).
In the electronic structure input file case, the geometries, energies, vibrational frequencies
or harmonic force constant matrices, and (optionally) higher-order force constants of the
reactant(s), product(s), saddle point, and generalized transition states are read in from unit
fu30, fu31, or fu40. (A more detailed statement of the available input options is given in
Section 9.) The number of points on the MEP available from electronic structure
calculations is usually small; thus when converging tunneling probabilities it is
Polyrate 64
sometimes necessary to extend the reaction path beyond the last input data point on one
or both sides of the MEP. This is done by specifying larger values for the SLM and SLP
keywords in the PATH section. The special interpolation procedures are described in
Subsections 9.C and D.
The generalized free energy of activation is then computed at each of the points on the
save grid (at which the reaction path information was saved), and the CVT rates are
calculated for an input set of temperatures (done in RATE). We find the maximum
generalized free energy of activation by local interpolation using 5-point Lagrangian
interpolation. The result calculated with 3-point Lagrangian interpolation is printed as a
check.
Various tunneling corrections can also be included by a call to KAPVA. The final output of
forward and reverse reaction rate constants with and without the various tunneling
corrections, as well as output of activation energies, analyses of bottleneck properties,
equilibrium constants, and the ratio of the CVT to the conventional transition state theory
rate constants, are provided by FINOUT.
If the VTST-IOC option is selected (DL keyword set to ic or ICOPT keyword specified),
the program will then update (done in ZOCUPD) all the MEP information based on
corrections calculated from the higher-level values read from the unit fu50 input file and
calculate a new set of rate constants based on the corrected values by the same
procedures as described above.
If the VTST-ISPE option is selected (DL keyword set to ispe), the program will update
the energies along the MEP based on a spline fit to the differences of the lower-level
energies and the higher-level energies read from the unit fu51 input file. A new set of
rate constants is then calculated, based on the corrected energies, by the same procedures
described above.
If the IVTST-0 method is selected, after the MAIN program reads all the information
provided at reactants, products, and saddle point, subroutine GIVTST is called. Then the
process of generating the information required at points along the reaction path by
interpolation is started using specific routines for IVTST instead of the ones employed
for calculations based on analytic potentials or fu30, fu31, and fu40 input files. If the
IVTST-1 method is selected, the electronic structure information at the stationary points
Polyrate 65
plus the data at an extra point located close to the transition state is read by the MAIN
program from file fu29 and then the subroutine GIVTST is called.
7.B. Determining the sign of s
If there is a saddle point, the reaction coordinate s is, by convention, positive on the
product side of the saddle point and negative on the reactant side. In the program,
however, the default is that s is defined as positive in the direction of the unbound normal
mode at the saddle point, and it is defined as negative in the opposite direction. When
one is using the hooks, the definition of the sign of s does not affect the calculated rate
constants when LCG3 or LCG4 calculations including tunneling into excited states are
not carried out, but it does affect the LCT probabilities when contributions from
tunneling into excited states are included, since the current coding of that case requires
consistency with the convention. When one is using fu30, fu31, or fu40, the choice of
SIGN also affects whether SCT calculations or LCT tunneling into the ground state are
correct, as explained in the next paragraph. Also, confusion might arise when one
specifies the range of the reaction path to be calculated or discusses the location of the
optimized variational transition state. We therefore advise users to override the default, if
necessary, to follow the established convention of s being positive on the product side.
The following procedure is recommended to ensure this. First, make a run without
computing the path (do not include the PATH section) and without computing the
properties of reactants and products (do not include REACT1, REACT2, PROD1, and/or
PROD2 sections), and look at the normal mode eigenvector corresponding to the normal
mode with imaginary frequency at the saddle point. If this vector points towards
products, set the SIGN variable keyword in the PATH section to product in full runs. If
not, set it to reactant (or omit it, since reactant is the default). There is another
keyword, IDIRECT, in the PATH section which determines the direction of the first step
from the saddle point in calculating the MEP. If SIGN is set correctly and if IDIRECT is set
to 1 (which is the default), the MEP toward the product side (which is determined by the
keyword SIGN discussed above) will be calculated first and the reactant-side MEP will be
calculated after the limit on the product-side MEP is reached. If SIGN is set correctly and
if IDIRECT is set to −1, the reactant-side MEP will be calculated first instead. The value
of IDIRECT should not affect the calculated results.
Polyrate 66
In practice, the SIGN variable works differently with the hooks and with files 30, 31, and
40. When one is using the hooks, SIGN actually changes the sign of the value of s that is
assigned to given geometry on the reaction path. When one is using the electronic
structure input file options, one cannot change the sign of s. However, it is still necessary
that SIGN be set correctly. If SIGN is set wrong, then the reaction path curvature at the
saddle point will not be computed correctly. The correct setting for SIGN when one is
using fu30, fu31, or fu40 is determined by the following rule: when using fu30, fu31, or
fu40, if the positive direction of s in the output is not associated with the direction toward
products, then change the choice for the SIGN variable in the PATH section of the input
and repeat the run.
7.C. Restart options
There are two ways to restart calculations in POLYRATE.
The first restart option is controlled by the RESTART keyword in the GENERAL section.
This option is designed to allow calculations at additional temperatures without
recalculating the information stored on the save grid. This option uses fu1. If the VTST-
IOC option is used with RESTART, one can change the lower level but not the higher level,
i.e., the fu50 file cannot be changed for the RESTART run. Furthermore, if the original run
was not a dual-level run, the restarted run cannot be a dual-level run.
The second restart option allows one to restart calculations without repeating all of the
work for the stationary points (reactants, products, and/or saddle point). This restart
option is controlled by the STATUS keyword in the REACT1, REACT2, PROD1, PROD2, and
START section. Each of the input sections for the stationary points (REACT1, REACT2,
PROD1, PROD2, and START) allows one to input optimized geometries, energies, and
frequencies from previous jobs. The user also has the option of only calculating
reactants, or only calculating products, or only calculating a saddle point to obtain the
optimized geometries, energies, and frequencies for the given stationary point before
proceeding with the rest of the calculation. Thus it is possible to optimize the stationary
points in separate runs, and then read in the data for those stationary points in later runs to
continue. To do this, the user can run Polyrate with only the *GENERAL, *ENERGETICS,
*SECOND, *OPTIMIZATION, *REACT1, and *REACT2 sections in the fu5 file. If the
calculation is a supermolecule calculation then both reactant 1 and reactant 2 must be
Polyrate 67
specified in the *REACT1 and *REACT2 sections. However, if the calculation is not a
supermolecule calculation then it is possible to calculate reactant 1 and reactant 2
separately using only the *REACT1 section and leaving out the *REACT2 section. Note
that when calculating only reactant 2, the information for reactant 2 is placed in the
*REACT1 section and the *REACT2 section is left out. The same scenario holds for
products, i.e., one can include *REACT1 or *REACT1 and *REACT2 but leave out *START.
If the user wishes to optimize the saddle point without optimizing the reactants and
products then the saddle point information is placed in the *START section and Polyrate is
run with only the *GENERAL, *ENERGETICS, *SECOND, *OPTIMIZATION, and *START
sections in the fu5 file. An fu61 file, which contains the optimized properties, is created
after every Polyrate run. The information on this file can be used to build a complete fu5
file or update an existing fu5 file with optimized information. Thus, effectively, one can
optimize each stationary point separately or in any combination of stationary points, add
the newly optimized information to an existing or a new fu5 file, and restart the
calculation to optimize the remaining stationary points or complete the full calculation.
See Section 12.A.6.
Polyrate 68
8. CALCULATIONS USING THE HOOKS
8.A. Methods for interpolating beyond SLM and SLP with the hooks
This section describes the procedures used when interpolating between the SLM end point
on the save grid and the reactants and between the SLP end point on the save grid and the
products, respectively. There are two procedures that are used. Note that SLM and SLP
keywords are only for MEP, and invalid for variable reaction coordinate.
The first procedure is used when the reaction being studied has a saddle point. (In this
case the SADDLE keyword in the PATH section is specified or taken as the default.)
Reactions with saddle points either do not involve interpolation, or they use the mapped
interpolation (MI) algorithm to extend the reaction path beyond SLM and SLP. The
options for this interpolation are controlled by the EXFIRST and EXSECOND keywords in
the PATH section. The MI algorithm is described in Sections 6.N.2, 6.N.3, and 10.J and in
Ref. 48 of Sect. 21.
The second procedure is used when the reaction being studied does not have a saddle
point. For this type of reaction the NOSADDLE keyword must be specified in the path
section. Reactions without saddle points always use a two-point extrapolation to extend
the reaction path beyond SLM and SLP. The options for this extrapolation are controlled
by the EXFIRST and EXSECOND keywords in the path section. The two-point extrapolation
is described in Section 10.A.
8.B. Zero of energy
In Polyrate the variable EZERO always denotes the energy that corresponds to reactants in
the potential energy subroutine, and it is used to convert the potential energy to the zero
of energy that is used in the rest of POLYRATE. EZERO refers to the energy of a single
reactant (for a unimolecular reaction) or the sum of energies of infinitely separated
reactants (for a bimolecular reaction). In the language of potential energy surfaces,
EZERO denotes the potential energy of the reactant or reactants at their classical
equilibrium geometries. In the language of electronic structure calculations, EZERO
denotes the sum of the electronic energy and the nuclear repulsion (for ab initio
calculations). It is necessary to understand this variable in order to understand the input
Polyrate 69
options available with the EZERO keyword in the GENERAL section; the rest of this section
provides the necessary explanation.
In Polyrate the user must ensure that EZERO is set equal to a value consistent with the
potential energy subprogram (when an analytic potential energy subprogram is used) or
with the electronic structure data (when the electronic structure input file option is used).
This can be accomplished in one of two ways: (i) by setting the EZERO keyword to
calculate and letting the program calculate the zero of energy, or (iii) by setting the
EZERO keyword to read and directly inputting a nonzero value for EZERO which is
consistent with the potential energy subprogram.
Setting the EZERO keyword to be equal to calculate causes the program to calculate
the zero of energy after the reactants have been optimized to their equilibrium geometries
at "infinite" separation. Because the zero of energy is not computed until the
optimization procedure, all energies for the reactant species which are printed to the long
output file on unit fu6 before the zero of energy is computed will have an incorrect zero
of energy. For a unimolecular system the zero of energy is set equal to the potential
energy of the system at its optimized reactant equilibrium geometry. For a bimolecular
system the zero of energy is set equal to the sum of the potential energies of the two
reactants after both reactants have been optimized to their equilibrium geometries. This
can be done with the SUPERMOL option by placing the two reactants at a large separation
distance given implicitly by the two geometries specified by the GEOM keyword in the
REACT1 and REACT2 sections of the unit fu5 input data file. (Note that, when the
SUPERMOL option is used, this sum is given by the energy at the end of the second
reactant's optimization).
8.C. User-Supplied analytic potential energy surface
8.C.1. Interface
The protocol of the subprograms for evaluating the potential energy from an analytic
function is as follows. The user must supply two subroutines, SETUP and SURF, which
accept and return all information from and to Polyrate in atomic units. The subroutine
SETUP has one integer type variable, n3tm, in its parameter list:
Polyrate 70
subroutine setup (N3TM)
In the argument list of the call statement to SETUP the Polyrate code passes the variable
N3TM where:
N3TM = 3 NATOMS
(This variable is used to dimension the arrays for the Cartesian
coordinates and the derivatives of the energy with respect to the
Cartesian coordinates for a given system.)
NATOMS = maximum number of atoms in the Polyrate code
(It is the actual number of atoms in the system set in the input
file.)
SETUP may optionally open data file(s) which contain the potential parameters, read these
parameters, set up any necessary data, and close any file(s) which were opened. SETUP is
called once and only once in each complete run of the program.
Note that SURF and SETUP are called by the hooks. In particular, SETUP may be called by
PREP and/or PREPJ, and SURF may be called by EHOOK, GHOOK, HHOOK, and OHOOK.
No other routines call SURF and SETUP.
Users should dimension arrays in SETUP carefully since inconsistency of array
dimensioning is the major potential source of error when passing information between
subprograms. Also, users should resolve any conflict in the assignment of the input and
output I/O units between Polyrate and SETUP. For the I/O unit numbers used by
POLYRATE, see Section 19. As noted there, unit 4 is reserved for use by the potential
routines, i.e., by SETUP. If SETUP requires more than one file, unit 7 is recommended for
the second file. Alternatively the FU# parameters in the aamod.f90 file can be modified
to avoid conflicts between the FORTRAN units used in Polyrate and those used by SETUP
and SURF. In addition, users should not name subroutines with the same name as an
existing Polyrate subroutine. A list of subroutine names and a short description of the
subroutines used by Polyrate are given in subsection 17.A.1.
The subroutine SURF evaluates the potential and its first derivatives as functions of the
Cartesian coordinates, and it has 4 elements in its parameter list. These are V, X, DX, and
N3TM, as follows:
Polyrate 71
subroutine surf (V, X, DX, N3TM)
where:
V = potential energy in hartrees
X = array of dimension N3TM which contains the Cartesian
coordinates in bohrs of all the atoms in the system
DX = array of dimension N3TM which contains the first derivatives (in
hartrees per bohr) of the energy with respect to each of the
Cartesian coordinates. DX should be determined analytically if
possible as all higher-order derivatives needed by Polyrate are
calculated numerically from these first derivatives.
N3TM = as defined above
The arrays X and DX must be of dimension N3TM within the subroutine SURF.
The order of the coordinates is (x, y, z) for atom 1, (x, y, z) for atom 2, ..., (x, y, z) for
atom N, where the order of the atoms is determined by the order used in the ATOMS list
keyword in the GENERAL section. (see Subsection 12.A.2).
Note that whenever the potential is read from FORTRAN unit fu30 file, SURF and SETUP
are not needed and may be replaced by their dummy versions, for example, those
included in the dumpot.f file.
During the calculation of the MEP, the quantities V, X, and DX are optionally written
(using the PRSAVERP keyword in the PATH section) by Polyrate to the file linked
to the FORTRAN unit fu6 for each point at which reaction path information is
saved (each save grid point). Since the user is often interested in the values of
additional quantities calculated by subroutine SURF (such as interatomic distances,
curvilinear internal coordinates, or various contributions to the potential energy)
at these save points, we also provide the array POTINF(NPOTPT) in rate_const
module in the Polyrate program as a means of passing such information from
subroutine SURF to the main program, in which the array POTINF is optionally
written to the file linked to the FORTRAN unit fu6. (This is controlled by the use
of the POTINF keyword in the PATH section). The maximum number of pieces of
Polyrate 72
data from the potential which may be printed at each save grid point is 99. Unlike
the parameter lists described above, the use of the common block SURFCM in the
user-supplied SURF subroutine is user-driven. The information stored in the array
POTINF is printed exactly as stored. Note that values assigned to the array POTINF
have no effect on any values calculated by POLYRATE.
8.C.2. Utility routines
The Polyrate program assumes that the user-supplied potential energy function
subprogram SURF accepts the values of the atomic Cartesian coordinates and returns the
potential energy and the derivatives of the potential energy with respect to the atomic
Cartesians. However, not all potential energy functions are written in terms of atomic
Cartesians; some potential energy functions are written in terms of bond lengths. With
this in mind, four utility subprograms are provided with POLYRATE. Two of the utility
subprograms are for three-body systems and the other two are for four-body systems.
Two types of utility subprograms are provided. One type converts atomic Cartesians to
bond lengths, and the other uses the chain rule to convert the derivatives of the energy
with respect to the bond lengths to derivatives with respect to the atomic Cartesians.
The subprograms COORD#, where # = 3 for a three-body system and # = 4 for a four-body
system, convert the atomic Cartesians to bond lengths. In the case of COORD3, nine
Cartesians are converted to three bond lengths. The order of the Cartesians and the bond
lengths are as follows:
X(1) — X(3): X, Y, Z for atom A
X(4) — X(6): X, Y, Z for atom B
X(7) — X(9): X, Y, Z for atom C
R(1): R(A−B)
R(2): R(B−C)
R(3): R(C−A)
The Cartesians are passed to COORD3 through the parameter list (X, N3TM) (X and N3TM
are defined in Subsection 8.C.1) and the bond lengths are passed to the potential
subprogram through the module POTCM3:
module potcm3
integer :: nsurf, nder, ndum(8)
Polyrate 73
real(8) :: r(3),energy, dedr(3)
end module potcm3
COORD3 assumes that all the coordinates (Cartesians and bond lengths) are in atomic
units. The subprogram also assumes that the potential is written such that the bond
specifications are as defined above. For example, if the potential for ClHBr is written
such that
R(1): R(Cl−H)
R(2): R(H−Br)
R(3): R(Br−Cl)
the user must define Cl as the first atom (atom A), H as the second atom (atom B), and Br
as the third atom (atom C) in the input data in unit fu5.
The subprogram COORD4 does the same calculation as COORD3 but for a four-body
system. In COORD4 the coordinates are defined as follows:
X(1) — X(3): X, Y, Z for atom A
X(4) — X(6): X, Y, Z for atom B
X(7) — X(9): X, Y, Z for atom C
X(10) — X(12): X, Y, Z for atom D
R(1): R(A−B)
R(2): R(A−C)
R(3): R(A−D)
R(4): R(B−C)
R(5): R(B−D)
R(6): R(C−D)
The subprograms CHAIN#, where # = 3 for a three-body system and # = 4 for a four-body
system, convert the derivatives of the energy with respect to the bond lengths to
derivatives with respect to the atomic Cartesians. In the case of CHAIN3, three derivatives
with respect to the bond lengths are converted to nine derivatives with respect to the
atomic Cartesians. The order of the derivatives is as follows:
DEDR(1): DEDR for the bond length A−B
DEDR(2): DEDR for the bond length B−C
DEDR(3): DEDR for the bond length C−A
DX(1): DEDX for atom A
DX(2): DEDY for atom A
Polyrate 74
DX(3): DEDZ for atom A
DX(4): DEDX for atom B
DX(5): DEDY for atom B
DX(6): DEDZ for atom B
DX(7): DEDX for atom C
DX(8): DEDY for atom C
DX(9): DEDZ for atom C
The derivatives with respect to the bond lengths are passed through the common block
POTCM as defined above, and the Cartesian information is passed through the parameter
list (X, DX, N3TM). This subprogram assumes the same definitions as COORD3.
The subprogram CHAIN4 performs the same calculation as CHAIN3, but for a four-body
system with the following coordinate definitions:
DEDR(1): DEDR for the bond length A−B
DEDR(2): DEDR for the bond length A−C
DEDR(3): DEDR for the bond length A−D
DEDR(4): DEDR for the bond length B−C
DEDR(5): DEDR for the bond length B−D
DEDR(6): DEDR for the bond length C−D
DX(1): DEDX for atom A
DX(2): DEDY for atom A
DX(3): DEDZ for atom A
DX(4): DEDX for atom B
DX(5): DEDY for atom B
DX(6): DEDZ for atom B
DX(7): DEDX for atom C
DX(8): DEDY for atom C
DX(9): DEDZ for atom C
DX(10): DEDX for atom D
DX(11): DEDY for atom D
DX(12): DEDZ for atom D
These subprograms can be used with any three- or four-body potential, which is written
in terms of bond lengths. For example, for a three-body potential made up of two
subprograms, PREPOT and POT, where PREPOT does the initializations for the potential, i.e.
performs the role of SETUP, and POT does the actual potential and derivative evaluations
given the geometry in terms of bond lengths, the user could provide SETUP and SURF
routines to link Polyrate with PREPOT and POT.
Polyrate 75
The subprogram SETUP would simply call PREPOT. For example:
subroutine setup (n3tm)
implicit double precision (a-h, o-z)
call prepot
return
end
The SURF subprogram would first call COORD3, then call POT, and then call CHAIN3 before
returning to the Polyrate program. For example:
subroutine surf (v, x, dx, n3tm)
implicit double precision (a-h, o-z)
use potcm3
dimension x(n3tm), dx(n3tm)
call coord3(x, n3tm)
call pot
v = energy
call chain3 (x, dx, n3tm)
return
end
8.D. Calculations using an electronic structure program through hooks
A very useful feature of the Polyrate program is its ability to link an electronic structure
program to obtain reaction path information directly. All energetic information needed
by Polyrate for single-level runs or for the lower level of a dual-level run is obtained in
one of two ways. The first way is via a set of general hook routines. The second way is
from an electronic structure file (fu29, fu30, fu31, or fu40). This section of the manual
describes the hook routines.
The hook routines are actually quite general. They can be used to call an analytical
potential surface, and this special case is described in section 8.C. Alternatively they
could be used for direct links to electronic structure programs (as in MORATE,
GAUSSRATE, GAMESSPLUSRATE, JAGUARATE, or NWCHEMRATE) or in any way that the user
finds useful. In the case of the connection to an electronic structure program, the user is
responsible for obtaining or writing the necessary routines that interface the hook routines
and the electronic structure program. In some cases, e.g., MORATE, GAUSSRATE,
Polyrate 76
GAMESSPLUSRATE, JAGUARATE, and NWCHEMRATE such interface routines have been
prepared by Polyrate developers, but users are invited to prepare their own interface
routines as well.
We note that historically Polyrate called SURF and SETUP directly. Beginning with
version 7.0, the hooks were inserted as an interface between the Polyrate program and the
source of potential information. The goal is for Polyrate to be completely blind as to
what happens on the other side of this interface. We refer to this as complete modularity
between the dynamics and the potential, and we believe that this modularity has been
fully accomplished since version 7.3.
The hook routines are PREP, PREPJ, EHOOK, GHOOK, HHOOK, and OHOOK. The source
code for these routines is located in the src/ subdirectory in hooks.f. This subdirectory
also contains six utility subprograms (YTRANS, YSECEN, YSECEP, YDERV2, YDER24, and
YNEWT). The role of each of the hooks is described below. Before proceeding with these
individual descriptions, we first make a few general comments. The basic concept of the
hooks is as follows: Whenever Polyrate needs an energy, it calls EHOOK. Whenever
Polyrate needs a gradient (or an energy and a gradient at the same geometry) it calls
GHOOK. Whenever Polyrate needs a Hessian (or a Hessian plus an energy and/or
gradient, all at the same geometry), it calls HHOOK. Polyrate has its own geometry
optimization routines, and it may employ them using energy, gradient, and/or Hessian
information from calls to EHOOK, GHOOK, and HHOOK. However, in many cases it is
more efficient to call external optimization routines. These can be accessed by calls to
OHOOK. Finally, we note that PREP and PREPJ are available for initialization tasks, i.e.,
for passing geometry-independent information to the other side of the interface.
The versions of the hooks distributed with Polyrate itself only call SURF and SETUP,
except for HHOOK, which calls GHOOK. This does not convey the full usefulness of the
hooks. The hooks are better appreciated by studying one of the direct dynamics codes
built on Polyrate, e.g., MORATE, GAUSSRATE, GAMESSPLUSRATE, JAGUARATE, and
NWCHEMRATE. But the Polyrate versions of the hooks provide clear examples of their
use that can be understood by all users, independent of whichever electronic structure
codes they are familiar with.
Since version 7.3, HHOOK computes Hessians by taking numerical derivatives of
gradients obtained by calls to GHOOK. The code is identical to the code for this purpose
Polyrate 77
on the Polyrate side of the interface. As mentioned in the previous paragraph, this does
not convey the full power of this hook. This hook is designed to allow the user to take
advantage of analytic Hessians if they are available. If analytical Hessians are available,
the user should modify HHOOK to use them. A similar generic version of OHOOK is also
provided.
PREP:
PREP is the driver for all preparation routines needed to set up the hooks. This routine is
called once after input file fu5 has been read in and before the table of input is written to
the output file. This call occurs before any calculations are done. This routine may be
used to call electronic structure preparation routines. File fu70 is reserved for use by
PREP.
To interface with a new electronic structure program one just needs to add a new block to
the ‘if block’ contained in this subroutine with a call to the appropriate routine. Note that
this is an optional hook. Not all electronic structure programs need initialization. When
PREP is not needed, one should use a dummy routine with a simple return command
inside.
PREPJ:
PREPJ is the species-dependent driver for all preparation routines needed to set up the
hooks. Any initializations that are dependent on whether the reactants, products, saddle
point, or generalized transition state is computed are done here. PREPJ is called up to six
times, namely it is called once each at the starts of the sections for REACT1, REACT2,
PROD1, PROD2, START, and PATH. In other words, PREPJ is called before each respective
reactant, product, or saddle point is studied and again before the reaction path is
computed. A variable, JTYPE, specifies which particular species is being computed; see
Section 19 on file usage.
To interface with a new electronic structure program one just needs to add a new block to
the 'if block' contained in this subroutine with a call to the appropriate routine. Note that
this is an optional hook. Not all electronic structure programs need any species
dependent initializations. When the PREPJ is not needed, user should prepare a dummy
routine with a simple return command inside.
Polyrate 78
EHOOK, GHOOK, HHOOK, and OHOOK always communicate with the Polyrate side of the
interface using mass-scaled Cartesians in bohrs and energies in hartrees. In the versions
of the hooks distributed with POLYRATE, either mass-scaled Cartesians or unscaled
Cartesians may be used for communicating with SURF. In the versions of SURF that are
distributed with POLYRATE, the energy is computed using the Cartesian coordinates, so the
hooks first convert to unscaled Cartesians before calling SURF. Similar transformations
are required for gradients and Hessians; for example, SURF returns gradients in unscaled
coordinates, but GHOOK converts them to mass-scaled coordinates.
EHOOK:
EHOOK is the energy interface subprogram of Polyrate.
To interface with a new electronic structure program, one needs to add a new block to the
'if block' with a call to an interface routine that accepts Cartesian coordinates (unscaled)
and returns the energy. If the read option is chosen for the EZERO keyword, then the
zero of energy should be consistent with the EZERO value specified in the input file.
Remember that the user must also specify the new interface potential by adding another
option to the POTENTIAL keyword and implementing the new possible value of the
associated IPOT variable in the FORTRAN code.
GHOOK:
GHOOK is the gradient (first derivative) interface subprogram of Polyrate.
To interface with a new electronic structure program, one needs to add a new block to the
'if block' with a call to an interface routine that accepts Cartesian coordinates (unscaled)
and returns the energy and first derivatives. The developer of a new interface must also
specify the new interface potential by adding another option to the POTENTIAL keyword
and implementing the new possible value of the associated IPOT variable.
HHOOK:
HHOOK is the Hessian (second derivative) interface subprogram of Polyrate.
For the second derivatives, the potential is specified by the HESSCAL keyword of the
SECOND section of the fu5 input file and is coded in FORTRAN using the IPOT variable.
If the keyword option ghook is used in the HESSCAL keyword, numerical difference
methods from Polyrate are applied; if the hhook option is used, then the second
Polyrate 79
derivatives are taken from HHOOK. The latter option is designed to allow HHOOK to
obtain analytic second derivatives from electronic structure routines. In the current
version of POLYRATE, the ghook and hhook options are essentially the same. If the
hhook option is used, the second derivatives are computed with the hooks routines
YSECEN and YSECEP, whereas if the ghook option is used, the second derivatives are
computed with Polyrate subroutines SECCEN and SECCEP. However, the numerical
methods used in YSECEN and YSECEP are the same as those in SECCEN and SECCEP.
HHOOK must convert the Hessian to mass-scaled coordinates before returning to the
Polyrate side of the interface.
To interface with a new electronic structure program, one needs to remove the subroutine
calls in the ISPOT equals to 1 block and add a new block with a call to an interface routine
that accepts Cartesian coordinates (unscaled) and returns the energy, first derivatives, and
Hessian matrix. Note one must ensure that the gradient and Hessian conform to the same
orientation. See subsection 12.A.4 for the description of the keyword options used to
calculate second derivatives.
OHOOK:
OHOOK is the geometry optimization interface subprogram of Polyrate. This routine
accepts an initial guess to the mass-scaled Cartesian coordinates of the full system and
returns the optimized geometry in mass-scaled Cartesian coordinates and the energy. A
variable, IOP, is used to specify which chemical species is being optimized: for IOP = 1,
or 2; the chemical species is reactant 1 or 2, for IOP = 3, or 4; the chemical species is
product 1 or 2; for IOP = 5, the chemical species is the saddle point.
The geometry optimization is specified by the OPTMIN and OPTTS keywords and is coded
in FORTRAN using the IGPOT variable. If the keyword option bfgs or nr is used for
either of these keywords, IGPOT is 0, and the optimization is performed by NEWT, which is
a Polyrate subroutine. The OHOOK option (IGPOT = 1) is designed to allow the OHOOK
routine to call an electronic structure package directly. In the generic version of the
OHOOK routine, the option calls YNEWT, which is supplied as part of the generic hooks.
(Notice that YNEWT is a slightly simplified version of the Polyrate routine NEWT.) To
interface with a new electronic structure program, one must replace the call to YNEWT
when IGPOT equals to 1 with a call to an interface routine that accepts Cartesian
coordinates (unscaled) and returns the optimized geometry and energy. Notice that, in
the current version of POLYRATE, the method used to optimize the minima and saddle
Polyrate 80
point should be the same (i.e. either both from Polyrate or both from electronic structure
package). For the description of the keyword options used in geometry optimization, see
subsection 12.A.5.
Polyrate 81
9. CALCULATIONS BASED ON AN ELECTRONIC STRUCTURE INPUT FILE
One major option of the Polyrate program is the ability to use MEP information obtained
from electronic structure calculations in the form of an input file instead of using an
analytic potential energy surface. This input file will contain MEP information for a
finite range of the reaction path, namely s in the interval [SLM, SLP]. It is the user's
responsibility to ensure that these input geometries do indeed lie on the MEP or a good
approximation to it.
When one of the electronic structure files (fu30, fu31, or fu40) is used the Polyrate
program is never supposed to make calls to the potential energy surface subprograms
SETUP and SURF. However, to satisfy all external references when linking the program
the subprograms SETUP and SURF must be provided. A potential energy surface file,
dumpot.f, distributed with the Polyrate program has been designed specifically for use
with this option of the code. This potential energy surface file contains dummy SETUP
and SURF routines which print a warning message and stop if subprogram SURF is called.
When the reaction-path information is calculated from electronic structure calculations
and is used as input for dynamical calculations, the necessary information (listed later in
this paragraph) is read from a separate data file which is linked to the FORTRAN unit
fu30, fu31, or fu40 and is keyed to the normal input in the file which is linked to the
FORTRAN unit fu5. Throughout this manual, unit fu30, unit fu31, and unit fu40 are
called the electronic structure input files. The input data in unit fu5 remains the same as
when the calculation is done with an analytic potential energy surface except that the
POTENTIAL variable keyword in the GENERAL section is set to unit30, unit31, or
unit40. A line-by-line description of the MEP input for unit fu30 is provided in
Section 12.C, a description of the input when using unit fu31 is given in Section 12.D.,
and a description of the input when using unit fu40 is provided in Section 12.E. Using
the information from unit fu30, unit fu31, and unit fu40, the quantities V(s), |I(s)|, w(s) ,
k3(s), k4(s), and BmF(s) are interpolated to locations on the save grid and are stored in
save grid arrays to be used for Lagrangian interpolation as needed for finding variational
transition states and as needed for tunneling calculations. The type of information used
to obtain the tables of the MEP quantities is as follows:
Polyrate 82
Potential
VMEP(s) is always read directly.
Determinant of the moment of inertia tensor
|I(s)| is always computed from the geometry of the complex. For reactants and
products at infinite separation |I(s)| is infinite, so for large |s| the program
interpolates the inverse of |I(s)| instead of |I(s)| itself. To obtain |I(s)|for finite s it
is necessary to read the 3N Cartesian coordinates R(s) or the mass-scaled ones
x(s).
Gradients
The gradient must be read in. The gradient is denoted DX. The code
has options to read either the gradient itself or the negative of the gradient, which is
the force. In addition, the gradient or force may be in either unscaled or mass-
scaled coordinates.
Frequencies
w(s) can be read directly or computed from the force constant matrix F(s). If
F(s) is read, both w(s) and the coefficient matrix L which diagonalizes F (or the
projected F) are obtained. A total of 3N-7 (for a nonlinear generalized transition
state), 3N-6 (for a linear generalized transition state), or 3N-1 (for solid-state or
gas-solid interface generalized transition state) frequencies or a 3N 3N force
constant matrix is read.
Anharmonicities
Either the cubic and quartic force constants k3(s) and k4(s) are read directly, or
they are omitted. If read, a total of 3N-7 (nonlinear), 3N-6 (linear), or 3N-1
(solid-state or interface) of each will be read. Even if k3(s) and k4(s) are not read,
anharmonicities can still be included by using the Morse I approximation.
Polyrate 83
Reaction-path curvature
The reaction-path curvature components BmF(s) can either be read in or they can
be computed from the gradients. These curvature components are needed for SCT
calculations but are not used for CVT or ZCT calculations.
The user should always supply the following information for all points on the Hessian
grid: s, VMEP , the geometry, the gradient, and either the frequencies or the Hessian.
Depending on the options chosen, one or more of the following should also be supplied
for all points on the Hessian grid: the frequencies, the Hessian (i.e., the matrix of second
derivatives of the potential), the cubic force constants, the quartic force constants, and the
curvature components. Alternatively, the curvature components can be calculated by the
program. For this purpose, when using files fu30 or fu40, the program can use only the
gradients at the save points or it can use the gradient at up to two additional s values on
either side of each Hessian point. However only the latter option is available when using
file fu31.
The user must also supply information about the reactants and the products, if it is
needed.
9.A. Relation of Polyrate input to electronic structure package output
GAUSSIAN94 prints the forces on the standard output file, and it prints the gradients on the
formatted check point file; however, on the latter the gradients are incorrectly labeled as
forces. We prefer to take the gradients from the formatted checkpoint file because
GAUSSIAN’s output format on the formatted checkpoint file is more similar to POLYRATE’s
input format (for fu30, fu31, and fu40), so the user can directly cut and paste.
A different issue arises when one uses the GAMESS electronic structure package. GAMESS
writes the gradient in both un-normalized and normalized form. Polyrate requires the un-
normalized gradient if one uses curvilinear coordinates, so the user should be sure to take
the gradient from the correct place in the GAMESS output.
Polyrate 84
9.B. Orientation of the molecule at generalized transition states
When an electronic structure calculation program is used to determine the optimized
structures for the generalized transition states, the electronic structure code sometimes
translates and/or rotates the molecule to a “standard”, a “Z-matrix”, or other orientation.
However, Polyrate requires precisely the orientation obtained by following the minimum
energy path in mass-scaled Cartesians. For example, if the ESD method is used, the
points along the path should be related by equations (26) and (27) of the GTST book
chapter [Ref. 5 of Sect. 21]. Using an incorrect orientation can introduce errors in the
gradients and curvatures and can result in errors in the tunneling calculations. The user
of Polyrate is urged to be very cautious in understanding these issues if he or she uses an
electronic structure package that re-orients the molecule. Special keywords are
sometimes required to prevent re-orientation.
For example, for single-point calculations that ask for a gradient or a Hessian or both,
when the GAUSSIAN input has the geometry in Cartesian coordinates and the NOSYMM
keyword is specified, then GAUSSIAN will not re-orient the molecule, and the gradients
and Hessians that it prints out in the formatted checkpoint file (Test.FChk file) are
consistent with the orientation of the input geometry. Notice that it is impossible to avoid
re-orientation of geometry if the Z-matrix is given in internal coordinates, since
GAUSSIAN automatically generates a set of Cartesian “Z-matrix” coordinates in which the
first atom is placed at the origin, the second one on the Z axis, and the third one in the X-
Z plane. This can be avoided using Cartesian coordinates for defining the input
geometry. A second aspect of GAUSSIAN the user should be aware of is that even when
using Cartesian coordinates for the input geometry in single-point calculations, if the
NOSYMM keyword is not specified, both the gradient and the force constants matrix
written to the formatted checkpoint file will correspond to a geometry translated and re-
oriented according to what GAUSSIAN calls the “standard orientation”. However, notice
that the forces and the force constants matrix printed out in the GAUSSIAN long output file
are still consistent with the initial input geometry orientation; thus they can be used for
dynamics without introducing errors in the calculation.
Re-orientation issues are more complicated when one considers reaction paths. It appears
to be impossible to generate a reaction path with GAUSSIAN without having the
geometries re-oriented if the transition state geometry required to perform a reaction path
Polyrate 85
calculation is input in internal coordinates. However, if the geometry of the transition
state is given in Cartesian coordinates, and if the computed force constants are also read
in Cartesian coordinates from a checkpoint file corresponding to a frequency calculation
performed including NOSYMM in the keyword list, the reaction path will have the correct
orientation to be used in a direct dynamics calculation. Whether the NOSYMM keyword is
or is not used in the actual reaction path calculation does not affect the origin or the
orientation of the respective points.
An alternative method that we have used in the past to generate the reaction paths is to
employ the electronic structure package GAMESS. However, although GAMESS can be
used to generate a non-re-oriented reaction path, we could not find a convenient way to
prevent GAMESS from re-orienting when it calculates the gradients and Hessians. (We did
find a way to avoid re-orientation, but it is inconvenient because it re-orders the atoms.)
One solution is to use GAMESS to generate un-re-oriented geometries along the reaction
path, and then use GAUSSIAN (with Cartesian coordinates input and NOSYMM) to generate
gradients and Hessians in a formatted checkpoint file. Our test of GAMESS were done
with the 9-11-96 version.
9.C. Methods for interpolation of electronic structure data with files fu30 and fu40
This section describes the procedures used with file fu30 when LOPT(2) is positive or with
file fu40 when MAXLPTS is positive.
For values of s between those on the input grid, the MEP quantities are obtained by n-
point Lagrangian interpolation. The maximum number of points used in the interpolation
is input to the program; the actual number of interpolation points is the minimum of this
input value [LOPT(2) in unit fu30] and the total number of points in the grid. Thus, if only
3 points are used in the grid, only up to second order Lagrangian interpolation can be
used.
For unimolecular reactions, association reactions, or reactions with wells, the reactant,
product, or well geometry (or both) will occur at finite values of s. In these cases
Lagrangian interpolation is also used for values of s approaching the reactant, product, or
well s value.
Polyrate 86
In runs using analytic potential energy functions, there are two grids: (i) the fine grid,
also called gradient grid, with step size s = SSTEP and (ii) the save grid, where
frequencies and the Hessian are calculated and stored, with step size s = INH * SSTEP.
See also sections 7, 10.D, and 12.A.7.
In runs using file fu30 or file fu40, there are three grids which are similar to the two grids
described above; however their use is somewhat different; also their step sizes are
determined differently. First is the gradient grid. This consists of all the s values at
which gradient information is read in records 35, 38, or 41 of unit fu30 or the equivalent
records of unit fu40. This grid is not required to be evenly spaced, so s does not exist,
and the SSTEP value read from fu5 is ignored. Second is the basic input grid, which is
called the sparse grid in Ref. 14 of Sect. 21. When using file fu30, this is the same as the
gradient grid if LOPT(6) 2; it is a subset of the gradient grid if LOPT(6) is 3 or 4. The
basic input grid is the grid of points for which one reads energies in record 31 of unit
fu30 and either frequencies (record 46) or Hessians (record 44). Third is the save grid.
Input electronic structure information and calculated reaction path curvatures are
interpolated from the basic input grid plus saddle point information to the save grid by n-
point Lagrangian interpolation. The step size for the save grid is s = INH * SSTEP. This
interpolation can also be done by the IVTST-M method (For unit fu30, LOPT(2) = –1; for
unit fu40, the MAXLPTS keyword in *GEN40 is set to –1) instead of by n-point Lagrangian
interpolation. When using the IVTST-M method with files fu30 and fu40, the
interpolation can only be calculated with the default IVTST-M options.
A comment on the calculation of BmF(s) may be helpful here. When an analytic potential
is used, and the default value (dgrad) is accepted for the CURV keyword, BmF(s) is
calculated by a quadratic fit of points on the gradient grid; this fit is carried out in
subroutine BCALC. In this fit, one uses points with s 0 to calculate BmF(s) for s –s,
and one uses points with s 0 to calculate BmF(s) for s +s . Then one interpolates
between –s and +s to get BmF(s = 0). Notice that none of the quadratic fits involves
data with both s > 0 and s < 0. Thus in eq. (98) [see Section 24.A, item 15],
d sign(s)[ ]vig (s){ } /ds becomes
sign(s)[ ]dvig (s) /ds. In contrast, when an electronic
structure input file is used, files fu30, fu31, or fu40, one calculates BmF(s) by a quadratic
fit to points on the whole gradient grid in subroutine RPHB. Since it is now possible for a
given 3-point quadratic fit to involve both negative and positive s, the sign(s) function
Polyrate 87
must be implemented before the fit is carried out because
sign(s)[ ]vig (s) is a continuous
function, but
vig (s) is not.
9.D. Methods for interpolation of electronic structure data with file fu31
This section concerns the procedures used with file fu31. The fu31 file is currently
incompatible with the IVTST0FREQ option. In version 2010, the ISPE and
FREQSCALE options are compatible. The default versions of these procedures may also
be used with file fu30 by setting LOPT(2) = –1 or with file fu40 by setting MAXLPTS = –1.
In runs using file fu31 there are also three grids, similar to those described above for files
fu30 and fu40, which store input and interpolated information. The gradient and the
basic input grids for file fu31 are the same as described above for files fu30 and fu40.
However, when using file fu31, the input grid information is always interpolated onto the
save grid using IVTST-M instead of by n-point Lagrangian interpolation. After data is
interpolated to the save grid, the rest of the calculation is the same as when using file
fu30 or fu40 or when using the hooks.
IVTST-M is described in Sections 6.N.2 and 10.J and in detail in Ref. 48 of Sect. 21.
Polyrate 88
10. SELECTED DETAILS OF THE CALCULATIONS
Most of the methods used by the program are described in detail, including equations, in
the GTST book chapter (Ref. 5 in Sect. 21). All methods not discussed in the GTST book
chapter are described in the present section of the manual. See also Refs. 14, 29, 30, and
47 in Sect. 21.
Subsections 10.A-10.L describe in detail various options that may be used with either of
the two kinds of calculations—those based on an analytic potential energy surface or
those based on an electronic structure input file.
10.A. Extrapolation of the reaction-path data beyond the range of the original grid
In some cases the variational transition state lies in the interval [SLM, SLP], which is the
range of the save grid, but the tunneling calculation requires information over a wider
range of s to converge.
For reactions with a saddle point this is handled almost automatically by the mapped
interpolation (MI) algorithm, which allows one to extend the range of the reaction path
used without calculating more energies, gradients, or Hessians. For reactions with a
saddle point the MI algorithm is available to interpolate the energy, the determinant of
the moment of inertia, the frequencies, and the curvature components between SLM and
the reactants or SLP and the products. This may be thought of as an interpolation between
SLM and reactants and an interpolation between SLP and products, or it may be thought of
as an extrapolation beyond SLM toward reactants and beyond SLP toward products. (That
is why we sometimes call it interpolation and sometimes call it extrapolation.) The end
result is that all information is interpolated over the entire range from reactants to
transition state to products. The keywords EXFIRST and EXSECOND in the PATH section
control the options for the interpolation. If the EXFIRST and EXSECOND keywords are not
specified then no interpolation is performed. The MI algorithm is explained in Sections
6.N.2, 6.N.3, 10.J, and 12.A.7 and in Ref. 48 of Sect. 21.
For reactions without a saddle point and using RP-VTST Polyrate includes a simple two-
point extrapolation to extrapolate the vibrationally adiabatic ground-state potential and
Polyrate 89
effective reduced mass,
meff , from the MEP end points to the reactants and/or products.
The asymptotic extrapolation procedures that may be used for reactions without a saddle
point are described in this subsection.
When using units fu30 and fu40 the two-point extrapolation is used by default to
extrapolate between the last save grid point and SLM or SLP. However, the IVTST-M
algorithm can be specified to interpolate between the last save grid point and SLM or SLP
by setting LOPT(2) = –1 for unit fu30 and by setting MAXLPTS = –1 for unit fu40. File
fu31 always uses the IVTST-M algorithm to interpolate from the last save grid point to
SLM or SLP. See Sections 6.N.2 and 10.J and Ref. 48 of Sect. 21 for more details about
the IVTST-M algorithm. In all cases, when using the electronic structure file input
options (units fu30, fu31, or fu40), the extrapolation or interpolation is applied using data
on the save grid, not the basic input grid (i.e., not the sparse grid). The extrapolation or
interpolation is specified by increasing the range of SLM and SLP in the path section.
Precise calculation of the transmission coefficients through the adiabatic barrier for
reactions involving two reactant or product species often requires calculation of the
ground-state (G) adiabatic energy
VaG (s) at large absolute values of the reaction
coordinate. But calculation of the MEP at large |s| is often impractical, especially in the
asymptotic regions near reactants or products, where a very small gradient step size is
often required for good accuracy because of the small magnitude of the gradient. To
alleviate this problem, the program contains an option to calculate
VaG (s) and
meff (s) at
large |s| by a two-point extrapolation method, controlled by the EXFIRST and EXSECOND
keywords in the PATH Section of the fu5 input when the hooks are used and the
NOSADDLE keyword is specified in the PATH section. This two-point extrapolation can
only be used for reactions without a saddle point or with electronic structure input files
fu30 and fu40. See the above discussion for more details. Here we discuss the method in
terms of
VaG (s), but the functional form is the same for
meff (s). [A similar extrapolation
is also made for
VMEP(s) but this is for informational purposes only, e.g., it may be
useful for plotting.]
The method used for bimolecular reactions when the calculation is based on a potential
energy surface involves a simple exponential function which is fit to the values of
VaG (s)
at the positive (s = SLP) or negative (s = SLM) limits of the reaction coordinate for which
VaG (s) has been accurately determined and to the adiabatic ground-state energies of the
products,
VaG (s = +¥) or reactants,
VaG (s = -¥). Thus
Polyrate 90
VaG (s) = Va
G (s = +¥) + VaG (SLP) -Va
G (s = +¥)[ ]e-a(s-SLP)
for extrapolation towards products (s > SLP), and
VaG (s) = Va
G (s = -¥) + VaG (SLM) -Va
G (s = -¥)[ ]ea(s-SLM)
for extrapolation towards reactants (s < SLM). The exponential range parameter is
supplied by the user, or the default (1.0
a0-1) can be used. Different values of can be
used in the same calculation for extrapolations towards products and reactants.
If the keyword EXFIRST and EXSECOND are not specified, or EXNSTP is zero, no
extrapolation is performed. This is equivalent to using a = ¥, i.e., this is equivalent to
setting
VaG (s) equal to its value at s = SLP for all s > SLP and to its value at s = SLM for all
s < SLM.
As far as inputting a value of , the user may use any method he or she likes to get .
One suggestion for guesstimating is a 2-point fit of the exponential on to the end of the
Hessian grid data: Let sx be a point near SLP (sx could be the second-to-last point, or
slightly farther back if precision of
VaG (s) info is lacking). Then require exponential to
fit VaG(s = sx ) and V sa
GSLP( )= , which gives
a =ln Va
G s = sx( ) -VaG s = +¥( )[ ]{ / Va
G s = SLP( ) -VaG s = +¥( )[ ]}
SLP - sx( )
However, if the value chosen for affects the results, then this represents the basic
uncertainty in the values; a wider range for
VaG (s) will be needed to obtain a better
estimation of .
10.B. Options for anharmonicity
In addition to the standard harmonic option, several anharmonic options are available
using the keywords SSTOR, TOR, MORSE, MORSEQQ, MORMODEL, QQWKB, QQSEMI, and
WKB. Anharmonicity may be included in reactants, products, or generalized transition
states, but only in conjunction with the independent-normal-mode (INM) approximation
Polyrate 91
in rectilinear coordinates except the SSTOR option. Two of these options, Morse I and
Morse I quadratic-quartic (MORSE and MORSEQQ respectively with the MORMODEL
variable keyword set to morsei), are described in the GTST book chapter (see pp. 87-92
of Ref. 5 in Sect. 21) and were first used in the calculations reported in Ref. 1 of Sect. 21.
The options defined by the QQSEMI and QQWKB keywords are two WKB options that will
be discussed in Subsection 10.B.1. The VARIABLE and VRANGE keyword options allow a
different anharmonicity method to be used for each mode in each region of the MEP.
When any of the above anharmonicity options are used, anharmonicity is computed for
all vibrational levels of a given mode by the same method. An additional anharmonic
option, specified by the WKB keyword, allows one to use a presumably more accurate, but
more time consuming method (the WKB method based on the true potential along each
generalized normal mode) for the ground-state energy level of each mode for modes
treated thermally, or for the specified energy level for state-selected modes. When this
option is chosen, the methods used for higher-energy states of thermal modes are still
determined by an additional anharmonicity keyword. If another anharmonicity keyword
is not included the higher-energy states will be determined using the harmonic
approximation. Details of the implementation of the WKB keyword option will be
discussed in Subsection 10.B.2. All WKB anharmonicity options are available only for
calculations based on the hooks. Whenever the WKB approximation is used, it is
employed in rectillinear coordinates, even if internal coordinates are used for the
frequencies and for non-WKB energy levels in the partition functions.
10.B.1. WKB anharmonicity based on a quadratic-quartic fit
When either QQWKB or QQSEMI keywords is specified, the program uses the primitive or
uniform WKB method, respectively, to compute the energy levels of a given generalized
normal mode vibration from a quadratic-quartic potential fit to the true potential. The
quadratic-quartic potential is determined by fitting to the potential computed at two
distances, specified by the user in the mass-scaled coordinate system, along the
generalized normal mode. The energy levels of this potential can be computed by either
a primitive WKB method [Ref. 21, Sect. 22] (QQWKB) or, for double well potentials, by a
semiclassical method using parabolic connection formulas [Ref. 22, Sect 20] (QQSEMI).
In these methods the phase integrals are calculated analytically. The calculations are
described in Ref. 17 of Sect. 21.
Polyrate 92
10.B.2. WKB anharmonicity based on the true potential
When the WKB keyword is specified, the program uses the WKB method to compute the
anharmonic ground- or first-excited-state energy levels of all generalized normal mode
vibrations from the true potential along the modes. The method is described in more
detail in Ref. 13 of Sect. 21. Note that WKB energy levels are not computed for reactant
and product diatomic species, but instead either harmonic or anharmonic energy levels
(as specified by the other anharmonicity options) are used.
Because the numerical solution of WKB eigenvalues requires repeated calculation of the
potential and may therefore be quite time consuming, this approach is used only for the
zero point (n = 0) eigenvalues for thermal modes or the specified energy level for state-
selected modes. Higher energy vibrational levels, used in the calculation of the partition
functions, are obtained by harmonic or anharmonic approximations discussed previously.
In particular, when the WKB-with-the-true-potential option is applied to evaluate the
ground-state energy levels, the vibrational partition function of a bound motion is
calculated as follows:
Qvib,m = e-e
0,mWKB /kT
+ e- n+1/2( ) wm /kT
n=1
¥
å
Qvib,m = Qvib,mHO - e- wm /2kT + e
-e0,mWKB /kT
where e0,mWKB is the WKB ground-state energy of mode m, and Q mvib
HO, is the vibrational
partition function in the harmonic oscillator approximation. If the harmonic frequency is
imaginary, the partition function is set to 1010. Note that in the WKB method the turning
points are determined during the calculation of the vibrational energies, and they can be
used directly in the calculation of the effective reduced mass as a function of s.
This method is used in the test runs oh3tr3, ohcltr2, ohcltr3, and ohcltr4.
10.B.3. Hindered rotor treatments
Torsions may be treated multi-conformer methods as explained in Refs. 53 and 63 or by
multi-structural methods that couple the torsions as explained in Refs. 89, 90, 92–96, 98–
Polyrate 93
105, and 113 of Sect. 21. These references explain the methods in detail, and they also
give original references. Note that we now recommend using MS-VTST or MP-VTST
rather than using the multi-conformer methods.
Beginning with version 8.2 of Polyrate, a torsional mode can be treated in the full
generality of Ref. 53. Please note the errata that have been added to Ref. 53. We label the
method developed in Ref. 53 as the Chuang-Truhlar (CT) method.
Beginning with version 2010 of Polyrate, several methods in Ref. 63 are also
implemented. These additional methods are the reference Pitzer-Gwinn (RPG) method,
the segmented- reference Pitzer-Gwinn (SRPG) method, the Ayala-Schlegel (AS)
method, and the segmented Ayala-Schlegel (SAS) method.
Beginning with version 2016, Polyrate can treat the torsional anharmonicity along
reaction path (saddle point and nonstationary points) by using coupled torsional
potentials in the multistructural method including torsional anharmonicity (MS-T(C)).
Note that only a single structure (SS) version is taken into account since only one saddle
point is given in a single Polyrate input file. Therefore we call this the SS-T method.
Multistructural (MS) effects should be taken into account separately by using the MSTOR
program.
There are two kinds of hindered rotor treatments: multiconformer (MC) methods and
multistructure (MS) methods. The MC methods involve identifying one or more of the
normal modes (or generalized normal modes) as a torsion about of specified bond. When
frequencies are required in MC methods they are normal-mode frequencies. The MS
methods do not require associating specific torsion with specific normal modes. When
torsional frequencies are required in MS methods, they are calculated in internal
coordinates based on a coupled model potential. In Polyrate calculations, only one
structure of the transition state or one reaction path is taken into account; therefore only
single-structure torsional potential anharmonicity (SS-T) along the reaction path is taken
into account.
Polyrate 94
10.B.3.a. Multiconformer methods
10.B.3.a.i. CT method
If mode m is treated as a hindered rotor (HR) by the CT method, its partition function
tends to the limit of a harmonic oscillator ( HOmQ ) at low temperature and goes to the limit
of a free rotor ( FRmQ ) at high temperature, and the interpolation is designed so that it
remains reasonably accurate for the hindered-rotor regime between these limiting cases.
The CT method is:
QmHR = Qm
MC-HO tanhQm
FR
QmI
æ
è ç
ö
ø ÷ ,
where the multiconformer harmonic oscillator (MC-HO) approximation for mode m is
QmMC-HO, the free rotor approximation for mode m is
QmFR, and I
mQ is an intermediate
result. They are given by
QtorMC-HO =
e-b (U j + wtor, j / 2)
1- e-b wtor, jj=1
P
å
QFR =(2pIkT)1/2
s
QI =e-bU j
bw tor, jj=1
P
å
where P is number of distinguishable minima along the torsion coordinate, is (kBT)-1,
kB is Boltzmann constant, Uj is the energy of the jth well relative to the global minimum,
tor,j is the torsional frequency of the jth well along the normal-mode or generalized-
normal-mode coordinate, I is the averaged torsional moment of inertia of the P minima,
is the total symmetry number ( = M/P, M is the total number of minima along the
torsion coordinate in the range [0, 2)). Note that usually P = 1 or P = M. Therefore, if
M/P is not an integer, the program prints an error message and stops. The CT method
approximates the one-dimensional hindered-rotator problem with a simple model
potential of the form
V =W
2(1- cos Mf)
where W is the height of the potential barrier, and is a coordinate that parameterizes the
internal rotational motion. For a potential of the above form with a geometry-independent
moment of inertia, the barrier height Wj, moment of inertia Ij, and one-dimensional
torsional frequency tor,j are interrelated by
Polyrate 95
wtor, j = MW j
2I j
æ
è ç
ö
ø ÷
1/2
If the frequencies tor,j are approximated as the same for all of the P minima and the
energies Uj are approximated as 0 (same as the global minimum energy) for all of the P
minima, we label this as single-frequency-and-energy (SFE) approximation. If only the
frequency is approximated as the same for all the distinguishable minima, we label it as
the single-frequency (SF) approximation. Otherwise, the treatment is labeled FULL.
Note that the single-conformer (SC) approximation in Ref. 52 is another name for the
special case of P =1. Therefore, starting from version 2010 of Polyrate program, this SC
approximation is not used as a stand-alone method.
10.B.3.a.ii RPG method
The torsional Pitzer–Gwinn method based on a reference potential gives the torsional
partition function as
QtorRPG =
1
P
QtorHO(wtor, j )
QtorCHO(wtor, j )
j=1
P
å QFR exp(-bW /2) I0(bW /2)
where
wtor, j is the frequency at the well j, W is the averaged barrier height of all the
wells to their left and right maxima, and
I0 is a modified Bessel function. If one uses the
frequency associated with the minimum of the 1D torsional reference potential to
approximate all the
wtor, j, this equation reduces to the Eq. 24 in Ref. 62. The reader is
referred to Ref. 62 for all further details.
10.B.3.a.iii. AS method
AS method uses a correction factor to adjust the RPG method
QtorAS =
1+ P2 exp[-bW /2]
1+ P1 exp[-bW /2]Qtor
RPG
where P1 and P2 are fifth order polynomial functions of
x º1/QFRand
y º bW /2 which
is given by Eq. 31 and 32 in Ref. 62.
Polyrate 96
10.B.3.a.iv. SRPG method
If the hindered-rotator potential does not closely resemble the form of
V =W
2(1- cos Mf), it may be convenient to decompose the partition function into a sum
of contributions from particular wells and to fit the potential between each peak and
minimum using a simple cosine line shape. For each well, the contribution may be
divided into the part to the left of the minimum and the part to the right of the minimum,
and each part of the classical partition function may be evaluated analytically. This is
referred as the segmented-reference classical (SRC) approximation, and it yields
QSRC = Q jSRC
j=1
P
å
where
Q jSRC = exp(-bU j )Q j
FR
´(f j - f j
L )
2pexp(-bW j
L /2)I0(bW jL /2) +
(f jR - f j )
2pexp(-bW j
R /2)I0(bW jR /2)
é
ë
ê ê
ù
û
ú ú
where Uj is the energy of the local minimum centered at j relative to the energy at the
global minimum,
W jL and
W jR are the left and right barrier heights located at
f jL and
f jR, respectively, and
Q jFR =
2pI jkT
s
Quantum effects may be approximated by the Pitzer-Gwinn approximation to yield the
segmented-reference Pitzer-Gwinn method
QtorSRPG =
Q jHO(wtor, j )
Q jCHO(wtor, j )
j=1
P
å Q jSRC
10.B.3.a.v. SAS method
The AS method has a segmented approach that is analogous to the SRPG method, and we
refer to this analog to the segmented Ayala-Schlegel (SAS) method, in which each
occurrence of
exp(-bW j /2) in the SRPG method is replaced by a term like
exp(-bW j /2)1+ P2(I j ,W j )exp(-bW j /2)
1+ P1(I j ,W j )exp(-bW j /2)
where P1 and P2 are given by Eq. 31 and 32 in Ref. 62.
Polyrate 97
The test runs ch4ohtr1, ch4ohtr3, ch4ohtr4, cwmctr2, cwmctr3, and h3o2fu31tr1 are
examples of using the hindered rotor options.
10.B.3.b. MS-T method
Starting from version 2016 of POLYRATE, the torsional-potential anharmonicity along the
MEP can be calculated using the MS-T method with a coupled torsion potential (i.e., MS-
T(C)), but only the input single transition structure is considered as generalized transition
states in the rate constant calculation; this is the SS-T treatment, i.e. Polyrate used by
itself does not compute the Multipath VTST (MP-VTST) rate constant, which requires
multiple transition structures in order to compute the variational and transmission
coefficients that correspond to their MEPs. Note that reactants and products are still
treated by harmonic oscillator approximation. To obtain rate constants calculated by the
full MS-T partition functions for reactants, products, and GTS, as well as the MP-VTST
rate constant, the user has to use MSTOR program (which is a separate program) to
calculate the rate constants at the conventional transition state and then use the variational
effects (ratio of CVT rate to TST rate) and transmission coefficients calculated by
Polyrate program (see the MSTOR manual for more details).
The conformational-rovibrational partition function using the MS-T method for a species
with J conformational structures is
Qcon-rovibMS-T = Q j
T j=1
J
å
QjT º Qrot, j exp -bU j( )Qj
QHTj
where Q jT
is the contribution of structure j to the rovibrational partition function with
torsional anharmonicity, Qrot, j is the classical rotational partition function for structure j,
U j is its relative potential energy, Q jQH
is its QH vibrational partition function partition
function, and Tj is a factor to account torsional-potential anharmonicity for all torsional
modes in the structure j. In particular, Tj is
Polyrate 98
Tj = 2p b( )t/2
w j,mm=1
F
Õ
w j,mm=1
F-t
Õ
detD j
M j,tt =1
t
Õ
exp(-bWj,h / 2)I0(bWj,h / 2)h=1
t
Õ
where t is number of torsional modes, F is number of bound vibrational modes (stretches,
bends, and torsions), w j,m and w j,m are respectively the normal mode harmonic
frequencies and the torsion-projected normal mode frequencies (both sets scaled), D j is
the moment of inertia matrix of Kilpatrick and Pitzer, M j,t is the periodicity of torsion
in structure j, Wj,h is the torsional barrier height based on a coupled torsional potential,
and I0 is a modified Bessel function. Note that for nonstationary points along a reaction
path j (starting from the saddle point j), the vibrational mode along reaction coordinate is
projected out and the torsional-potential anharmonicity Tj is calculated for each
nonstationary points where Hessian is calculated or available. Therefore, vibrational
partition functions of points along reaction path includes the torsional-potential
anharmonicity and then torsional-potential anharmonicity is taken into account for
searching variational transition state.
To calculate Tj , one only needs to input the set of M j,t values for torsions and projected
frequencies have to be calculated using non-redundant internal coordinates.
10.C. Alternate method for the calculation of numerical second derivatives
In order to calculate the Hessian matrix, the second derivatives of the potential with
respect to the Cartesian coordinates are computed numerically, using the analytic first
derivatives supplied by the analytic potential energy surface subprogram. By default, the
method of central differences is used to compute these second derivatives. The formula
is given by equation (16) in the GTST book chapter (Ref. 5 of Sect. 21).
Two alternate options, selected by setting the NUMTYP variable keyword to quadratic
or fourth, were added for use in cases where the default method may lead to numerical
instability. In the most accurate option, NUMTYP = fourth, the second derivatives are
computed by fitting the analytic first derivatives to a fourth order polynomial. For
NUMTYP = quadratic, the second derivatives are computed from a quadratic fit of the
potential.
Polyrate 99
The parameters NUMSTEP and DLX2, which are specified by the variable keywords
NUMSTEP and DLX2 respectively, in the input file which is linked to the FORTRAN unit
fu5, determine the step size for calculating second derivatives of the potential, and, if
needed, for cubic and quartic force constants as well. The second derivatives are needed
for two purposes: locating stationary points and computing vibrational potentials.
The DLX2 parameter is used for locating the stationary point, and the NUMSTEP parameter
is used for calculating the force constants. When anharmonicity options are chosen that
require cubic and quartic force constants, which are third and fourth derivatives of the
potential, these are evaluated as numerical second and third derivatives, respectively, of
the analytic gradient. The step size used for these numerical derivatives is always
NUMSTEP.
10.D. Reaction-path following methods
Our recommendations, as described in Ref. 27 of Sect. 21, for the most appropriate
methods for calculating the MEP and the reaction-path information required for
variational transition state theory calculations with semiclassical transmission coefficients
are as follows: (i) the Page-McIver algorithm, with the Hessian recalculated at every step,
and with a cubic starting step, (ii) the ES1* algorithm (the ES1 method with DELTA2 =
SSTEP and DIFFD = 0.01) with a Hessian step size three times larger than the gradient step
size, and with a quadratic starting step, and (iii) the Euler steepest-descents (ESD)
algorithm with a Hessian step size nine times larger than the gradient step size, and with a
quadratic starting step. The RPM keyword in the PATH section allows the user to choose
between the above possibilities or to choose other methods for computing the MEP. A
list of all methods available in this version is as follows:
The RPM keyword is set to esd for the ESD method. This method is discussed further in
Ref. 18 of Sect. 21.
The RPM keyword is set es1 for the ES1 method of Ref. 18 of Sect. 21. This is an
improved version of the methods proposed by Ishida et al. [Ref. 19, Sect. 22] and by
Schmidt, Gordon, and Dupuis [Ref. 20, Sect. 22]. The ES1 method allows for a user-
selected criterion for whether or not a stabilization is carried out.
Polyrate 100
The RPM keyword is set to pagem for the Page-McIver method, which is called the local
quadratic approximation (LQA) in the original reference [Ref. 17, Sect. 22], for
calculating the MEP.
The RPM keyword is set to vrpe for the VRP method based on the Euler steepest-
descents algorithm for the zero-order step, which is called VRP(ESD). This method is
discussed further in Ref 49 of Sect. 21.
The ESD, ES1, and Page-McIver methods can be used with the RODS algorithm [Ref.
47, Sect. 21], to reorient the generalized-transition-state-theory dividing surface. This is
done by adding the RODS keyword in the PATH section of file fu5. The RODS algorithm
is not recommended for use with the VRP(ESD) algorithm since the generalized-
transition-state-theory dividing surface has already been optimized by the VRP(ESD)
algorithm.
Each of the above methods can be used with either a quadratic first step (i.e., a first step
along the imaginary-frequency normal mode) or a cubic starting algorithm in which the
first step off the saddle point is based on a cubic expansion of the potential energy surface
using the imaginary-frequency normal mode eigenvector and the curvature vector. This
is specified by the FIRSTSTEP variable keyword also in the PATH section. For a quadratic
first step set FIRSTSTEP = nmode and for a cubic first step set the variable to cubic.
A discussion of the above methods and useful hints for choosing the most appropriate
one, especially for direct dynamics calculations, is given in Ref. 27 of Sect. 21.
We use the following conventions for the step size of the save grid. The save grid is
defined as the set of points where the frequencies are stored for straight VTST runs, these
are also the points where the Hessian matrix is calculated and where generalized
transition-state normal mode analyses are performed and saved. The INH keyword
determines how many gradient steps are taken before a Hessian is calculated or read in.
In other words, the step size of the save grid is required to be an integer multiple, INH, of
the gradient grid step size. Hence, the save grid step size = INH SSTEP.
There is another option, which is specified by the SFIRST keyword, in which the first
NFSTEP steps are taken with a different gradient step size FSIZE. Then the gradient step
size, SSTEP, is used for the remaining steps.
Polyrate 101
10.E. Interpolation of small-curvature effective reduced mass
For the small-curvature tunneling calculations (SCT), the effective reduced mass is
needed. The default method for computing the effective reduced mass from the values
stored on the Hessian grid, which includes s = 0, is spline interpolation. An alternate
method, selected using the LAGRANGE keyword within the SCTOPT list of the TUNNEL
section of the input is Lagrangian interpolation of order n. This new method is
recommended when using medium-to-large Hessian grid step sizes for which spline fits
tend to oscillate. The step size used for either of the interpolation methods is INH SSTEP
specified by the user with the SSTEP and INH keyword in the input data file. The alternate
method is used in the sample runs described in Subsections 16.C.3, 16.C.9, and 16.C.29.
10.F. Reaction-path curvature calculation
See Section 6.H for a brief introduction to reaction-path curvature.
When the CURV variable keyword in the PATH section of the input is set to oneside or
dgrad, the calculation of the component BmF(s) of the reaction-path curvature along the
direction of mode m at a point s on the reaction path Hessian grid, is carried out by eq.
(98) of the GTST book chapter. (This is equivalent to the second form of eq. (47) of [Ref.
17, Sect. 22].) This method requires the computation of the derivative of the gradient of
the potential with respect to the reaction coordinate s (see pages 96-98 in the GTST book
chapter). In early versions of the polyatomic VTST code this derivative was computed
using one-sided forward differences; see eq. (105) of the GTST book chapter. An option,
CURV = dgrad has been added to use a more accurate method, namely, central
differences (which is equivalent to a 3-point quadratic fit). When this new option was
added the one-sided difference method was changed to one-sided backward differences to
allow for a more consistent set of algorithms. It is recommended, however, that the
method of backward differences, CURV = oneside, never be used. The step size used
for these numerical derivatives is that of the gradient grid, SSTEP.
Another option, CURV = dhess, calculates the reaction-path curvature components using
eq. (48) of Page and McIver [Ref. 17, Sect. 22]. This method does not require the
Polyrate 102
derivative of the gradient. A sample run with this option is discussed in Subsection
16.C.4. Preliminary tests indicated somewhat higher accuracy with dgrad.
For any of these choices of CURV, the code does not compute the curvature at s = 0
directly. Instead, the curvature at s = 0 is computed linear interpolation as described by
the INTMU keyword in the PATH section.
10.G. Solid-state and gas-solid interface reactions
A solid-state reaction, which includes gas-solid interface reactions as a special case, is a
reaction in which N primary atoms are considered to move in the presence of a fixed
solid. This is called the embedded cluster model; see Ref. 9 of Sect. 21. For solid-state
reactions, the SPECIES should be ssrp or ssts as explained in section 6.B.
10.H. VTST-IOC calculation, including ICR, ICL, and ICA schemes
The original VTST-IOC method is the VTST-IOC method that is described in Ref. 36 of
Sect. 21, and the modified version that was the default in Polyrate from version 7.2 –
7.9.2 is described in Ref. 44 of Sect. 21. In this manual we use the phrase VTST-IC to
refer to any scheme involving interpolated corrections from a higher level and VTST-
IOC to refer to any VTST-IC scheme in which the data for corrections involves a higher-
level optimization. Thus VTST-IC and VTST-IOC can involve not only the original ICA
scheme of Ref. 36 of Sect. 21 for interpolating corrections to frequencies but also to the
ICR and ICL options described in Ref. 44 of Sect. 21 and also described toward the end
of this section. To use any IOC method, the user has to prepare an input file (unit fu50;
see Subsection 12.F) which contains the necessary higher-level information. The DL
keyword must be set equal to ioc and/or the ICOPT keyword must also be given in the
GENERAL section of the unit fu5 input file.
If the MEP is finite (unimolecular reaction with a single product) or semi-infinite
(unimolecular reaction with two products or bimolecular reaction with a single product)
or has wells (i.e., precursor and/or successor complexes) that the user wishes to use in the
interpolation (i.e., if MEPTYPER or MEPTYPEP is (or both are set to well), the user has to
Polyrate 103
tell the program where the MEP ends and/or some properties of the complexes
corresponding to the wells (see Subsection 12.F).
The VTST-IOC method demands an explicit matching of the frequencies, i.e., the user
must indicate which mode at the saddle point corresponds to each mode at the other two
stationary points involved in the interpolation (or else accept the default as explained
later in this paragraph). For a bimolecular reaction with two products (MEPTYPER and
MEPTYPEP are both set to two), the recommended method is to let the program match the
frequencies in descending order (which is the default in the current version), i.e., the
highest frequency at the saddle point is matched to the highest frequency of either of the
two asymptotic species, and so on. If the user knows (by symmetry and/or by inspecting
the uncorrected MEP output) that the matching should not be done in descending order,
then the user can use the FREQMAT keyword to input the matching order manually in unit
fu50. When MEPTYPER and MEPTYPEP are not both set to two, one of the normal modes
at the reactants and/or products turns into the reaction coordinate motion, and the user has
to specify the frequency matching explicitly, so the FREQMAT keyword must be used.
If a well is used for interpolation on the product side of the MEP, and the user is not
interested in the reverse rate constant, then the accurate product information is not
required. The user can use the NOPRODFREQ keyword to tell the program that no
correction for the product frequencies is needed. Otherwise the user has to use the
PRODFREQ keyword to input the corrected frequencies for the product in unit fu50.
The original IOC method involved the ICA option, which corrects all the frequencies, and
sometimes it will generate a negative correction that changes a small real frequency into a
negative frequency (not an imaginary frequency). In order to prevent this unphysical
result, one may use IVTST-0 for one or more low frequencies, or, preferably, one may
use one of two new interpolated correction options, namely the ICL (Interpolated
Correction based on Logarithm of ratios) and the ICR (Interpolated Correction based on
Ratios) options.
We note that all three IOC interpolation options for frequencies correct the lower-level
frequencies only when they are real. If the lower-level frequencies are imaginary, the
program does nothing, so the frequencies remain imaginary. (The recommended way to
handle this situation is to use the LOWFREQ option in the fu50 file. This option treats
Polyrate 104
selected low-frequency vibrations by IVTST-0, while carrying out the rest of the
calculation by the VTST-IOC method.)
The differences between the original ICA option and the ICL and ICR options are best
illustrated by equations. Let
wmLL(s), m = 1, 2, ..., F-1 (where
F = 3N -6 for an N-atom
nonlinear generalized transition state) denote the lower-level frequencies of the
generalized transition state at s. In the original IC method, which is called “interpolated
corrections–additive” (ICA), the dual-level (DL) frequencies are given by
wmDL(s) = wm
LL(s) + f ICA(s)
where
f ICA(s) = interpolant wmHL(s) -wm
LL(s){ }s=-¥,0,¥
.
The “interpolated corrections based on the ratio” (ICR) and “interpolated corrections
based on the logarithm” (ICL) methods are defined by
wmDL(s) = wm
LL(s) f ICR(s)
where
f ICR(s) = interpolant wmHL(s) /wm
LL (s){ }s=-¥,0,¥
and
wmDL(s) = wm
LL(s)exp f ICL(s)[ ]
where
f ICL(s) = interpolant ln wmHL(s) /wm
LL(s)[ ]{ }s=-¥,0,¥
.
There are also options for interpolating V sMEP ( ) . The original option, called SECKART,
is described in Ref. 36 of Sect. 21. In the DECKART option, the dual-level V sMEP ( ) is
defined as:
VMEPDL (s) = VMEP
LL (s) + VEckHL(s) -VEck
LL (s)[ ]
where
VEck (s) =AY
1+ Y+
BY
(1+ Y)2+ C
Y = exps - S0
L
æ
è ç
ö
ø ÷
A =VMEP(s = +¥) -VMEP(s = -¥)
C =VMEP(s = -¥)
B = (2V¹ - A - 2C) ± (V¹ - C)(V¹ - A - C) ;
we choose
Polyrate 105
S0 = -L lnA + B
B - A
æ
è ç
ö
ø ÷
so that the maximum of
VEck (s)occurs at s = 0.
V ¹is the classical barrier height, and L is
the range parameter. In
VEckHL(s), L is determined from the imaginary frequency of the
higher-level calculation by the equation
LHL =2V ¹(V ¹ - A)
m(w¹)2B
where µ is the scaling mass (normally set to 1.0 amu), and w¹
is the imaginary frequency
at the higher level. In VEck
LL(s), L is determined from a four-point fit to V sMEP ( ) at
reactants, products, saddle point, and one extra point as discussed in Refs. 36 and 44 in
Sect. 21.
Versions 7.2 – 7.9.2 used the so-called improved scheme (i.e. icl for vibrations and
deckart for V sMEP ( ) ) as the default VTST-IOC method. Beginning with version 8.0
the defaults are icl and seckart. To perform the calculation by the original IOC
method, a combination of ica and seckart was required. The Eckart function fit to 3
stationary points and
w¹ at the higher level can only be used for bimolecular reactions.
The following table summarizes the IOC options for interpolating corrections to
vibrations an to the VMEP curve:
Option no. Keywords
1 ica, seckart
2 icl, deckart
3 icl, seckart
4 icr, seckart
5 ica, deckart
6 icr, deckart
Option 1 was the original default, option 2 was the recommended choice and default in
versions 7.3 – 7.9.2, and option 3 is the current recommended choice and default.
In order to perform VTST-IOC calculations using any of the ica, icl, or icr choices
for interpolating vibrational information, we suggest the following procedure for a
bimolecular reaction:
Polyrate 106
Step 1. Calculate the rate constants at the lower level. At the end of the reaction path
section in the long output file (i.e. before the reaction rate calculation), the
range parameter L is calculated automatically from a four-point fit. In the
same section, an L value obtained from the imaginary frequency at the lower
level is also calculated, but this is only for comparison.
Step 2. Input the range parameter L calculated from the four-point fit as the value for
the RPL keyword in the fu50 input file. Or calculate the range parameter L for
the RPL keyword in the fu50 input file with the findl.f program in /util. (See
Sect. 15.D.) This utility program asks the user to input the
VMEP values at
reactants, saddle point, and products (0, barrier height, endoergicity) and the
(s,
VMEP) values of an extra point which lies somewhere between s = – and
s = 0 (between the reactants and saddle point).
Step 3. Use the RESTART keyword to calculate the rate constants from the interpolated
corrections with the higher-level information given in fu50. (Note: The
RESTART option is not working properly in this version, you must do the
lower-level calculations again if you are dealing with an analytic surface.)
For a unimolecular reaction, the B parameter can be calculated from the findb.f program
in /util.
10.I. VTST-ISPE calculation
The VTST-ISPE method for calculating reaction rates is a dual-level approach. ISPE
denotes that the higher-level information consists of interpolated single-point energies.
The fully converged reaction path is calculated at a lower level of theory Y, e.g.
MP2/6-31G, and single-point energies are calculated at a higher level of theory X, e.g.
CCSD(T)/cc-pVDZ, where the geometry for the single-point calculation is taken from
level Y, denoted X//Y. In order to circumvent the limitation of the VTST-IOC formulas
that are designed for calculations in which only corrections at stationary points are used,
the VTST-ISPE calculations use the mapped interpolation formulas rather than the
VTST-IOC formulas. However, whereas the IVTST-M method requires at least one
nonstationary point on both sides of the saddle point, VTST-ISPE can handle the case
where corrected energies are provided only at one nonstationary point on either side of
the saddle point.
Polyrate 107
To calculate the reaction rates with the VTST-ISPE algorithm, one should calculate a
converged reaction path at the lower level Y. Then a spline under tension is used to
interpolate the energy difference of a few single-point level-X energies along the level-Y
MEP and the energy from the lower level Y (i.e., V VX/ /Y Y- ). As in our previous
interpolated variational transition state theory with mapping (IVTST-M) method, a
mapping function is used to provide a systematic interpolating procedure for both
bimolecular and the unimolecular reaction. Like IVTST-M, which does not support LCT
calculations at this time, VTST-ISPE supports only ZCT and SCT tunneling options at
this time.
To map the reaction coordinate s into the z space, the following expression is used:
÷ø
öçè
æ -
p=
L
ssz 0arctan
2 (1)
Information from the lower level is used to obtain the parameters s0 and L for the
mapping. First we calculate
RWR,X;)()0(
2
XMEPMEP0
A =mw
-=-=
¹
sVsVs (2)
and
PWP,X;)()0(
2
XMEPMEP0
B =mw
-==
¹
sVsVs (3)
where m is the scaling mass, is the imaginary frequency of the saddle point at the
lower level, and R, RW, P, and PW denote the reactants, the reactant well, the products,
and the product well at the lower level. Then we calculate
( )0
B
0
AA 2,min sss -= (4)
and
( )0
B
0
AB ,2min sss -= (5)
Finally, the parameters s0 and L are obtained as:
2
BA0
sss
+= (6)
and
2
BA ssL
+-= (7)
The parameters s0 and L obtained from equations (5) and (6) are used in equation (1) to
map the reaction coordinate s into z. For a unimolecular reaction with a unimolecular
Polyrate 108
product (A → B), where the reaction coordinate s occupies a finite interval, this maps a
finite interval in s into a finite interval in z. For a bimolecular reaction with bimolecular
products (A + B → C + D), where the s variable occupies interval [-, ], the mapped z
values are located in the finite interval [-1, 1]. For A → B + C or A +B → C, equation
(1) maps a semi-infinite interval of s to a finite interval of z. In all cases, a spline fit to
the differences of the classical energies is applied with this finite range of z. Therefore,
we can write the interpolated energy along the reaction path at the dual level as:
V V V zDL LL spline= + ( , )D (8)
where DL means dual level (VTST-ISPE), and LL means the lower level. V is the
difference of the classical energies between higher-level and lower-level at a particular s
value.
In the current version of POLYRATE, ISPE calculations may be used with the ZCT and
SCT tunneling methods but not with LCT or OMT.
To carry out a VTST-ISPE calculation, an external file fu51 is used to input the values of
the higher-level energies. Please refer to Section 12.G for a description of fu51. The
VTST-ISPE method can be applied with higher-level calculations at only the reactants,
products, and saddle point, or it may be applied with more points. In the latter case, extra
points are used to correct the energies along the MEP, the POINT sections are required for
the extra points.
The interpolation can be carried with or without the wells along the MEP. It is
recommended to use the well option if there is a complex along the MEP in order to
obtain the best interpolation. For bimolecular reactions, the energies of the saddle point,
wells, products, and extra points that are input via fu50 should be with respect to the sum
of the energies of the reactants at the higher-level (which is set to zero). There are two
test runs using the VTST-ISPE method, the ch5fu51tr1 test run which is a bimolecular
reaction with the J1 surface, and the cmctr3 test run, which is a unimolecular reaction
with two wells. For both reactions, we use the two turning points at the representative
energy of the SCT calculation at 300 K as the extra points, and we evaluate the single-
point energies with the MP2/6-31G** method.
The VTST-ISPE method can be applied for a minimum of three high-level points, namely
the reactants, saddle point, and products. The calculations are performed using unit fu51
with the stationary points being required in the ISPEGEN section of unit fu51, and the
Polyrate 109
POINT section being included if and only if additional points along the reaction path are
added. A POINT section is needed for each additional high-level point along the reaction
path.
See Ref. 51 of Sect. 21 for more discussion.
10.J. Alternative methods for mapped interpolation
The mapped interpolation (MI) methods for IVTST-M calculations and for extrapolation
beyond SLM and SLP are described in Ref. 48 of Sec. 21. In addition to the standard
methods described in that paper, Polyrate contains a few variants that may be used to test
sensitivity to the approximations made in interpolation.
The first variant concerns the interpolation of VMEP(s) when there is only one reactant or
product or when interpolation is based on a well. The default is to use a cubic
polynomial in s to fill in 10 points between the end of the grid and the finite-distance
stationary point. Variant 1, with the nopolys option for the IVTSTMOPT keyword in the
PATH section of the fu5 input file, replaces the 10 points that in the standard algorithm are
calculated from a local cubic polynomial by a single point located a small distance (s)
from the reactant (or product or well), whose energy is approximated using the lowest
frequency at the stationary point. Thus the spline under tension is fit to 14 + m or 5 + m
points rather than 23 + m points. (See Ref. 48 for the definitions of m and other details.)
The second variant allowed in MI calculations is an alternative way to calculate the
effective reduced mass for CD-SCSAG calculations. The standard way involves
interpolating each curvature component. The alternative method, keyword INTMUEFF in
the GENERAL section of the fu31 input file, involves interpolating the argument of the
exponential function in eq. (16) of Ref. 48 instead of interpolating curvature components.
When the INTMUEFF keyword is used in conjunction with a VTST-IOC calculation, no
higher-level correction to μSC(s) will be made. The INTMUEFF keyword is only available
when using unit fu31.
Polyrate 110
10.K. Quantized-reactant-state tunneling calculation
For unimolecular reactions at low temperatures, most of the reactant molecules have their
reaction-coordinate generalized vibrational modes in the ground state. Thus the
semiclassical treatment, which assumes continuous tunneling energies, is inappropriate.
Starting in version 6.2, we have included a new method that performs the tunneling
calculations only at the energies corresponding to the eigenstates of the reaction-
coordinate mode of the reactant for the case of a unimolecular reaction. (Note that all
other modes are still assumed to be in their ground states.) The reaction-coordinate
eigenstates can be determined using the harmonic or WKB approximation. Details of the
theoretical background and an application to the diffusion of hydrogen atoms on a Ni
surface can be found in Ref. 37 in Sect. 21. The keywords used to perform this type of
tunneling calculation can be specified in the TUNNEL section in the unit fu5 input file.
See Section 12.A.8 under the keyword QRST for details.
10.L. Curvilinear generalized normal mode analysis
The generalized normal mode analysis that is performed at each Hessian grid point (see
Section 9.C) on the MEP may be carried out either in Cartesian coordinates or in internal
coordinates. The COORD variable keyword in the PATH section makes it possible to select
the type of coordinates to be used. The default option for the COORD variable keyword is
cart which specifies Cartesian coordinates. (It is very important to use curvilinear
coordinates rather than Cartesian coordinates for VTST calculations; Cartesian
coordinate will very likely yield imaginary frequencies along the reaction coordinate,
which will cause unphysical VTST results.) Two options are available to select a
generalized normal mode analysis in nonredundant curvilinear coordinates: curv1 and
curv2. If either of the curvilinear internal coordinate options is selected for COORD, the
Cartesian gradient vector G and force constant matrix F at the save point are first
transformed to the curvilinear internal gradient vector g and curvilinear internal force
constant matrix f using equations 30 and 31 in Ref. 37 of Sect. 22 or using equations 10
and 11 in Ref. 46 of Sect. 21.
When the option curv1 is selected, the method of Ref. 41 of Sect. 21 is used for the
generalized normal mode analysis. The option curv1 is only available for
nonredundant internal coordinates for reactions involving a total of three atoms, and it
Polyrate 111
may be used whether or not the geometry along the reaction path is linear. When the
curv1 option is chosen, the curvilinear internal coordinates—two stretches and a
nondegenerate bend for nonlinear triatomics or two stretches and a degenerate bend for
linear triatomics—are automatically defined by the program. In this method, the B
matrix and C tensor are constructed using the difference Cartesian coordinate formulas
from Pariseau et al. [Ref. 38, Sect. 22] for the bond stretch and nonlinear valence bend
coordinates and from Hoy et al. [Ref. 39, Sect. 22] for the degenerate linear bend
coordinate. The difference Cartesian B matrix and C tensor are then transformed to
Cartesian coordinates.
When the option curv2 or curv3 is selected, the method of Ref. 43 or 46 of Sect. 21 is
used for generalized normal mode analysis. The options curv2 and curv3 can be used
for any number of atoms, but curv2 is used for nonredundant internal coordinates, and
curv3 is used for redundant ones. Note that stretch, nonlinear or linear bend, and
dihedral curvilinear internal coordinates are allowed for this method. (The extension to
linear bends was presented in Ref. 45 of Sect. 21.) When the curv2 option is chosen,
the user is required to define the curvilinear internal coordinates used for the curvilinear
generalized normal mode analysis via the INTDEF keyword. In this method the Cartesian
B matrix and C tensor are constructed by using explicit FORTRAN statements [Ref. 40,
Sect. 22] for the B matrix and C tensor derived by Challacombe and Cioslowski [Ref. 41,
Sect. 22], except for the linear bend case where the derivation is presented in Ref. 45 of
Sect 21. If the curvilinear internal coordinate is a doubly degenerate linear bend, a
symbol “=” is used to indicate the connections between atoms within the INTDEF
keyword.
Next, at a nonstationary point along the MEP, the curvilinear internal force constant
matrix f is projected as
Polyrate 112
fp = 1-p(BuBT)[ ]f 1- (BuBT)p[ ],
where
p =ggT
gT(BuBT)g,
before applying the Wilson GF method [Ref. 36, Sect. 22] of vibrational analysis to
obtain frequencies and generalized normal modes. The matrix u is a (3N 3N) matrix
with the reciprocal of each inverse mass appearing three times for each atom on the
diagonal, and the matrix B is the Wilson B matrix.
If POTENTIAL = unit30 or unit40 (see Section 12.A.3), normal mode analyses at
stationary points are always carried out in Cartesian coordinates. If POTENTIAL = hooks,
normal mode analyses at minima are carried out in Cartesian coordinates, and the normal
mode analysis at the transition state is carried out in curvilinear coordinates. Note that
options for anharmonicity (e.g., TOR and MORSE keywords in Section 12.A.6) have not
been implemented for curvilinear internal coordinates. Therefore, keyword options
curv1, curv2 and curv3 should not be used with anharmonicity options.
At stationary points, one should obtain the same frequencies by using either curvilinear or
rectilinear coordinates, except for small differences due to round off. However at non-
stationary points the generalized normal mode frequencies do depend on the coordinate
system — see Refs. 25, 41, 43, 45, and 46 in Sect. 21. (It is very important to use
curvilinear coordinates rather than Cartesian coordinates for VTST calculations;
Cartesian coordinate will very likely yield imaginary frequencies along the reaction
coordinate, which will cause unphysical VTST results.)
In the current version, both curv1 and curv2 are restricted to use a nonredundant set
of internal coordinates. Redundant internal coordinates are always chosen by the option
curv3. In POLYRATE, the number of curvilinear internal coordinates cannot exceed 3N-6
for the curv1 and curv2 options. The option curv3 allows the number of internal
coordinates to be as large as 3N + 6.
10.M. IVTST0FREQ option
Polyrate 113
In some cases, we found that the directly calculated frequencies of the lowest real-
frequency modes are not stable or not accurate along the reaction path, and this can cause
problems in evaluating the zero point energies, partition functions, and tunneling
probabilities. To ameliorate this problem, we have added a new scheme for interpolating
frequencies. This scheme is called IVTST−0-for-frequencies; it is a single-level analog
of the method used for interpolating differences of frequencies in the VTST-IC method
[Ref. 36, Sect. 21]. In the IVTST−0-for-frequencies scheme, the interpolation procedure
has one of four possible forms, depending on the molecularity of the end points of the
interpolation. Unimolecular reactions always have a molecularity of one at the negative s
terminus. Interpolations for bimolecular reactions may have molecularity two at the
negative s terminus, or − instead of extending all the way to reactants, the interpolation
may extend only to a reactant-side well where the molecularity is one. Similar
considerations apply on the product side.
MEP type 1. Bimolecular/bimolecular interpolation
A bimolecular/bimolecular interpolation is for a reaction that has two reactants and two
products. Either there are no wells present on either side of the reaction path or (more
likely) wells are present but are not used in the interpolation, i.e., they are not recognized.
There are two functional forms used for this case,
a. If )( Rww >¹ and )( Pww >¹
or if )( Rww <¹and )( Pww <¹
, where
)0( ==¹ smm ww , )( -¥== smR ww , and )( +¥== smP ww , an Eckart function is used
to approximate the frequencies along the reaction path:
mmm
m CY
YB
Y
YAs +
++
+=
2)1(1)(w (1)
where
)()( -¥=-+¥== ssA mmm ww (2)
Bm = (2wm¹ - Am - 2Cm) ± 2 (wm
¹ - Cm)(wm¹ - Am - Cm)[ ] (3)
)( -¥== sC mm w (4)
÷÷
ø
öçç
è
æ -=
L
SsY
m,0exp (5)
÷÷ø
öççè
æ
-
+-=
mm
mmm
AB
BALS ln,0 . (6)
Polyrate 114
Unlike the original VTST-IC algorithm, we use a single-level analytical expression for
estimating the value of L instead of using a fit involving a lower level. The analytical
expression is [Ref. 26, Sect. 21]
B
AVVL
2
2
)(
)(2
¹
¹¹ --=
wm (7)
)()( MEPMEP -¥=-+¥== sVsVA (8)
)(MEP -¥== sVC (9)
B = (2V ¹ - A - 2C) ± 2 (V ¹ - C)(V ¹ - A - C)[ ] (10)
)0(MEP ==¹ sVV (11)
where MEPV is the potential energy along the reaction path, and ¹w is the imaginary
frequency at the saddle point.
b. If )( PR www >> ¹ or if )( PR www << ¹
, a hyperbolic tangent function is
used to approximate the frequencies along the reaction path:
mm
mm EL
TsAs +÷
÷
ø
öçç
è
æ -=
,0tanh
2
1)(w (12)
where
2
)()( -¥=++¥==
ssE mm
mww
(13)
÷÷ø
öççè
æ
-
+-=
m
mm
x
xLT
1
1ln
2,0 (14)
m
mmm
A
Ex
-=
¹w2 (15)
c. For cases where two consecutive of the three frequencies are the same (i.e.,
Rww =¹or Pww =¹
, a constant value or used at one side of the reaction path and a
symmetric Eckart function fit is used on the other. For example, if PR www ¹= ¹, then
îíì
>++
£=
0)1/(
0)( 2
R
sYYB
ss
mPm
w
ww (16)
where
)(2)2( PP wwww -±-= ¹¹mmmB (17)
÷ø
öçè
æ=
L
sY exp (18)
and L2 is given by eqs. (7)−(11).
MEP type 2. Two reactants to one product (or well)
Polyrate 115
We introduce the notation P−W which denotes the product or the well, whichever is
being used as the right-side edge of the interpolation region. In this type of reaction the
function used to fit the frequencies depends on the s value, which is in the range of
WP-<<¥- ss .
a. If s < 0, a hyperbolic tangent function is used to approximate the frequencies as
described in the previous section for base 1b.
b. If WP0 -££ ss , a cut-off hyperbolic tangent is used to approximate the
frequencies:
mm
mm Ess
s
L
TsAs +
÷÷
ø
ö
çç
è
æ
÷÷ø
öççè
æ
-
-=
-
-
WP
WP,0tanh
2
1)(w (19)
where mA , mT ,0 , and mE are the same as previous section. L is evaluated using eqs.
(7)−(11). This makes )(smw continuous with one continuous derivative.
If ¹= mm ww R, or WP, -¹ = mm ww , then the value of R,mw or W- P,mw is modified by ± 2
cm−1 to make the function monotonic.
MEP type 3. One reactant (or well) to two products
This type of reaction is similar to type II but the functional forms are reflected
through s = 0.
MEP type 4. One reactant (or well) to one product (or well)
We introduce the notation R−W which denotes the reactant or the reactant-side well,
whichever is being used as the left-side edge of the interpolation region.
a. If )( W-Rww >¹ and )( W-Pww >¹ or if )( W-Rww <¹ and )( W-Pww <¹ , two
cut-off Gaussian functions are used to approximate the frequencies along the reaction
path:
xm
x
xmxmm C
s
s
BAs ,2
,,
1
exp)( +
÷÷÷÷÷÷
ø
ö
çççççç
è
æ
÷÷ø
öççè
æ-
-=w ; x = R-W,P-W (20)
)exp()( ,, xmxmxm BA ww -= ¹ ; x = R-W,P-W (21)
xxmC w=, ; x = R-W,P-W. (22)
The parameter xmB , is evaluated using a single-level analytical expression rather than a
fit to a lower-level surface. In particular we use
Polyrate 116
Bm,x =sx2m w¹( )
2
2 V ¹ -Vx( ); (23)
b. If ¹= mm ww W-R, or ¹= mm ww W-P, then the frequency is set equal to a constant
on one side of the saddle and approximated by a symmetrical cut-off Gaussian is used for
the other side on the reaction path. For example, if WP,W-R, -¹ ¹= mmm www , then the
frequency is set to W-Rw when 0£s and evaluated using eqns. (20−23) when s > 0.
c. If )( W-PW-R www >> ¹ or if )( W-PW-R www << ¹ , a cut-off hyperbolic
tangent function is used to approximate the frequencies along the reaction path.
mm
mm Ess
s
ss
s
L
TsAs +
úúû
ù
êêë
é
÷÷
ø
ö
çç
è
æ
-÷÷ø
öççè
æ
-
-=
-
-
-
-
WR
WR
WP
WP,0tanh
2
1)(w (24)
where mA , mT ,0 , and mE are determined by eqns. (2,13−16), and L is evaluated using eq.
(7).
The keyword option IVTST0FREQ is used to apply the IVTST0FREQ method for
interpolating the vibrational frequencies along the path. If either side of the reaction path
is unimolecular or if one recognizes an intermediate structure (indicated by *WELLR or
*WELLP sections), then an arc distance from saddle point has to be provided for the
interpolation (by using the SR and SP keyword options).
The equations in this section are not currently published; the only available reference is
this manual.
10.N. LCG4 option
Beginning with version 8.6, the options LCT3 and LCT4 are both available, but one cannot
use both of them in the same run. These two options replace the previous LCT option.
The LCTOPT keyword includes four new options.
The option vadavg can be used with LCT3 or LCT4, and it averages the vibrationally
adiabatic potential in a doubly vibrationally adiabatic region. Specifically,
Veff (x) = VeffIII(˜ s 0,xI) +
x -xIII
xI -xIIIVeff
I (˜ s 0,xI) -VeffIII(˜ s 0,xIII)[ ]
Polyrate 117
where III and I indicate the beginning and end of the region that overlaps. The default
is novadavg and the vibrational adiabatic potential in this region is given by
Veff (x) = min VeffIII(˜ s 0,xIII),Veff
I (˜ s 0,xI)[ ]
The option vefsrch numb only can be used with the LCT4 option, and it switches on
the search for nonadiabatic regions that are completely adiabatic in the LCT3 method. In
particular, it becomes operative at the tunneling energy after (higher than) that for which
the last nonadiabatic region was found according to the LCG3 algorithm, and the search
is carried out for a total of numb energies beginning at that point. The search locates the
maximum of the vibrationally adiabatic potential at a given tunneling energy and
compares the value with the actual potential. If the actual potential is smaller than the
adiabatic potential, then the procedure ends, otherwise the nonadiabatic region is
extended until the vibrationally adiabatic potential is smaller than the actual potential.
The default is vefsrch 999 because this search is required for correct LCG4
calculations. There is also an option called novefsrch that is equivalent to vefsrch
O.
For example, if 80 linear paths are calculated, and the 40 lowest-energy paths have
nonadiabatic regions in LCG3, setting numb equal to 20 will cause the program to search
for nonadiabatic regions along paths 41–60. This avoids the search for nonadiabatic
regions along the 20 highest-energy paths where it is likely that nonadiabatic regions may
exist only due to round-off; it allows one to avoid extra calculations at these energies
very close to the effective barrier top because they have no significant effect on the
results.
A restart option has been added, and it is described by two new keywords in LCTOPT. In
particular, lctstr stores the information in unit fu49 (this is the default), and
lctsrst restarts a calculation from unit poly.fu48. An old calculation stored in fu49
can be restored directly if fu49 is renamed as fu48. The default is nolctrst. If
lctrst is specified, but the unit poly.fu48 does not exist, the program stops
automatically. With lctrst the LCTOPT options have to be the same as in previous
calculations, that is, ngamp and ngtheta cannot be changed.
Polyrate 118
To incorporate the restart option in Polyrate the modules were modified. The old LCG3
subroutine (renamed in version 8.5 as LCG) reads from unit fu48 and stores the
information in the common block LCRST1 which is linked to LCVEF.
This restart option will work in POLYRATE, MORATE, and GAUSSRATE. When the restart
option is used with GAUSSRATE, the restarting data for the LCT calculation will be read
from fu48 instead of esp.fu83.
This restarting procedure is simple and flexible, and it allows the use of an old LCG3
fu48 file to restart an LCG3 calculation or to start a new LCG4 calculation, or vice versa.
All the combinations are possible. The restart option is specially useful when we want to
calculate tunneling into vibrational accessible excited states. In a first run we can do the
calculation of the ground state large curvature transmission factor. This information is
saved in unit FU49. We can include tunneling into vibrationally excited final states in a
second run if still worth it after looking at the output.
Further details of the LCG4 algorithm are provided in Ref. 54 in Sect. 21.
10.O. MS-VTST, MP-VTST, FMS-VTST, and FMR-VSTT calculations by using
both the Polyrate and MSTOR programs
For molecules and transition states that have multiple conformations generated by
torsions, we recommend MS-VTST [61], MP-VTST [62,63,72], FMS-VTST [68], or
FMP-VTST [68] calculations. Such calculations can be carried out by making runs with
Polyrate and MSTOR programs. The MSTOR program [64-66] is a program for applying
the internal-coordinate torsional anharmonicity method [70,71,68] for treating torsional
anharmonicity (MS-T); it is available as a separate package at
http://comp.chem.umn.edu/mstor/.
The internal-coordinate torsional anharmonicity method is a practical thermochemical
method for including multiple structures and torsional anharmonicity to calculate
conformational–vibrational–rotational partition function for complex systems. This
scheme obviates the need of earlier approaches to identify torsional motions with specific
normal modes, and it approximately accounts for coupling of torsional modes to one
another and to other modes. It includes the conformational free energy associated with
the existence of multiple structures (conformations) and the additional effects of torsional
Polyrate 119
potential anharmonicity. The original paper [70] included methods based on a subset of
structures as well as the method using all structures. The method containing all structures
was originally call MS-AS, but now we usually use all structures and, as explained in ref.
[64], we simply refer to the method employing all structures as MS-T.
In the original papers introducing MS-VTST [61] and MP-VTST [62,63,72], we
included multistructural torsional anharmonicity only at stationary points; tunneling
transmission coefficients and recrossing transmission coefficients were calculated in the
quasiharmonic (QH) approximation. (A quasiharmonic calculation is one that uses the
harmonic oscillator formulas for vibrational partition functions but with effective (scaled)
frequencies rather than the harmonic frequencies; the effective frequencies are usually
chosen to improve the estimate of the zero point energy [69].) In Ref. [68] we introduced
the capability to include multistructural anharmonicity all along the reaction path. To be
precise, we will label calculations by the original methods as MS-VTST [61] and MP-
VTST, and we will label calculations with multistructural anharmonicity all along the
reaction path [68] as full MS-VTST (FMS-VTST) and full MP-VTST (FMP-VTST).
In carrying out MS-VTST and MP-VTST calculations, Polyrate is used to carry
out single-structure quasiharmonic (SS-QH) calculations for reaction paths. In carrying
out FMS-VTST and FMP-VTST calculations, Polyrate is used to carry out single-
structure quasiharmonic what we shall call single-structure torsion (SS-T) calculations.
Throughout this discussion, we use the word structure as a synonym for conformation.
An SS calculation involves a single conformational structure of each reactant and a single
conformational structure of the transition state. SS-QH calculations use the QH
approximation along the reaction path, and SS-T calculations use the MS-T
approximation along the reaction path.
A note about chirality: when one is carrying out a single-structure calculation to
compare with experiment, if the structure has a distinguishable mirror image, then one
needs to include an extra factor of two in its rate constant, as discussed elsewhere [67].
However, in this section, we literally mean a single structure and the factor of two is not
included in such a case.
Some preliminaries about notation: (1) When we say "variational effects" we
mean the difference between a variational transition state theory calculation and a
conventional transition state theory calculation. In MS-VTST, MP-VTST, FMS-VTST,
and FMP-VTST calculations, variational effects are included by multiplying a
conventional transition state theory rate constant by a transmission coefficient that is
called a recrossing transmission coefficient. (2) The methods explained here may be used
with a variety of approximations for the tunneling, for example, ZCT, SCT, LCT, OMT,
Polyrate 120
or LAT. In general we use the abbreviation MT ("multidimensional tunneling") to refer to
any of these. (3) In our original paper
This subsection explains how to perform MS-VTST, MP-VTST, FMS-VTST, and
FMP-VTST calculations by combining results from Polyrate and MSTOR. In brief, the
MSTOR program is used to perform all the calculations for the stationary points (reactants,
saddle points, and products), and Polyrate is used to perform SS-QH or SS-MP reaction
path calculations to obtain variational effects and transmission coefficients.
In order to carry our either an MS-VTST or an MP-VTST calculation, the first
step is to find all the conformational structures of the transition state (that is, all the
saddle points leading from reactants to products along parallel reaction paths (as
contrasted to reaction paths in series)) and all the structures of the reactant or reactants.
Structures of the transition state are called transition structures, and structures of the
reactant(s) are called reactant equilibrium structures or just reactant structures. Next one
numbers the transition structures so that the lowest-energy one is called k =1, and in
another list one orders the reactant equilibrium structures so that the lowest-energy one is
called k = 1. The energy difference between the lowest-energy transition structure and the
lowest-energy reactant equilibrium structure is called the classical barrier height, V‡ .
Then one uses MSTOR to calculate MS-T partitions functions for the transition
state and the reactant(s). For the reactant of a unimolecular reaction, this partition
function is called QMS-T, R . For the reactants of a bimolecular reaction, the product of
the partition functions of the two reactants ( QR1 and QR2 ) is also called Q
MS-T, R , but
the quantity we will need to calculate rate constants in the bimolecular case is F (the
partition function per unit volume) rather than Q (the partition function) so that one has to
convert Q to F when calculating bimolecular rate constants. Note also that it is possible
that MS-T will be used for only one of the two reactants. If the reactant R2 does not have
torsion, then one may use a simpler method, for example, the harmonic or quasiharmonic
approximation, for QR2
. Then FMS-T, R
is the bimolecular reactants’ partition function
per unit volume (with its zero of energy at the sum of the potential energies of the lowest-
energy reactant structures), and QMS-T, R
is the total partition function of a unimolecular
reactant (with its zero of energy at the potential energy of the lowest-energy reactant
structure).
The partition function for the transition state is called QMS-T,‡
. Note that this
partition function is sum over contributions from distinguishable structures:
Polyrate 121
QMS-T,‡
= QkT,‡
k=1
K
å (1)
where K is the number of distinguishable conformational structures of the transition state,
and QkT, ‡
is the rovibrational partition function of saddle point k with torsional potential
anharmonicity (T). Note that the difference in energy between the zero of energy used for
the transition state partition functions QkT,‡
and that used for the reactant partition
function is taken here to be the classical barrier height, which is the potential energy of
the lowest-energy conformational structure (k = 1) of the saddle point minus the potential
energy of the lowest-energy equilibrium structure of the reactant.
The next step is to perform one or more SS calculations with POLYRATE; this is
explained next.
10.O.1. MS-VTST
The MS-VTST rate constants including multidimensional tunneling are given by
the following formulas for a bimolecular reaction and a unimolecular reaction
respectively:
kbimolMS-CVT/MT = k1
QHG1QH-CVT kBT
h
Qelec‡ Qk
T,‡
k=1
K
å
FMS-T, R
exp(-bV‡) (2)
kunimolMS-CVT/MT = k1
QHG1QH-CVT kBT
h
Qelec‡ Q
kT,‡
k=1
K
å
QMS-T, R
exp(-bV‡) (3)
where k1QH is the quasiharmonic tunneling transmission coefficient for the reaction path
passing through transition structure 1, b is 1/ kBT , kB is Boltzmann’s constant, T is
temperature, h is Planck’s constant, Qelec‡ is the electronic partition function of the
conventional transition state (which is denoted as ‡); and the CVT recrossing
transmission coefficient for structure 1 is G1QH-CVT , which is given by the ratio of the
quasiharmonic CVT rate constant for the reaction path through transition structure 1 to
the quasiharmonic conventional TST one for transition structure 1.
In order to obtain k1QH and G1
QH-CVT , one performs an SS-QH calculation with
POLYRATE. The k1QH is printed out in the Polyrate output file and G1
QH-CVT is calculated
Polyrate 122
G1QH-CVT =
k(1),QH-CVT
k(1),QH-TST (4)
10.O.2. FMS-VTST
An FMS-VTST calculation is the same as an MS-VTST one except for the
transmission coefficients. One replaces k1QH and G1
QH-CVT by k1T and G1
T-CVT , which
are obtained by running SS-T calculations in Polyrate with the keyword SSTOR. In
particular, the recrossing transmission coefficient G1T-CVT is calculated as
G1T-CVT =
k(1),T-CVT
k(1),T-TST (5)
10.O.3. MP-VTST
In MP-VTST, we calculate the transmission coefficient as a properly weighted
average over tunneling transmission coefficients and variational transmission coefficients
for several reaction paths instead of calculating transmission coefficients only from one
path as is done in MS-VTST. This subsection gives the procedure to perform MP-VTST
calculations.
The MP-VTST rate constants including multidimensional tunneling are given by
the following formulas for a bimolecular reaction and a unimolecular reaction
respectively:
kbimolMP-CVT/MT =
kBT
h
Qelec‡
FMS-T, R
exp(-bV‡) kkQH G
kQH-CVT Q
kT,‡
k=1
K
å
» gkBT
h
Qelec‡ Qk
T,‡
k=1
K
å
FMS-T, R
exp(-bV‡)
(6)
kunimolMP-CVT/MT » g
kBT
h
Qelec‡ Q
kT,‡
k=1
K
å
QMS-T, R
exp(-bV‡)
(7)
where the MP-VTST generalized transmission coefficient is approximated by
Polyrate 123
g =
kkQH Gk
QH-CVT QkT,‡
k=1
P
å
QkT,‡
k=1
P
å
(8)
To evaluate the quantities in these formulas, we have to make P runs of Polyrate (where
P ≤ K), one for each of the P user-selected distinguishable structures of the transition
state (note that these structures are numbered by k = 1, ..., P). Each of the runs gives a
quasiharmonic CVT rate constant k(k ),QH-CVT , a quasiharmonic conventional TST rate
constant k(k ),QH-TST, a quasiharmonic tunneling transmission coefficient kkQH , and a
quasiharmonic CVT recrossing transmission coefficient GkQH-CVT . The first three are
printed in the Polyrate output file, and the fourth is given by
GkQH-CVT =
k (k ),QH-CVT
k (k ),QH-TST
(9)
The other quantities needed for MP-VTST rate constants can be calculated by using the
MSTOR program.
Note also that GkCVT is independent of which reactant structure is used, but the
choice of reactant structure affects the lower-energy limit of the integration used to
calculate kk , and thus it could affect the values calculated for the rate constants at low
temperature. Therefore all the additional Polyrate runs (k = 2, ..., P) needed to upgrade
MS-VTST to MP-VTST should use structure k of the transition state and the lowest-
energy structure of the reactant(s). Note that one has to calculate a reaction path long
enough to make sure the kk is converged. In case the saddle point k is connected with a
reactant(s) conformation much higher in energy than the lowest-energy structure of the
reactant(s), there is possibilities that the kk is overestimated because of the program is
trying to integrate kk to the lowest-energy structure of the reactant(s). This is one aspect
if the calculation that needs to monitored carefully if calculations are made at low
temperature.
Note that the wavy equal sign in equation (6) can be replaced by a straight equal
sign if P equals K. When P = 1, the MP-VTST rate reduces to the MS-VTST rate.
Alternatively one also can calculate the MP-VTST rate constants by the following
procedure. Let’s define the multistructural torsional anharmonicity factors for reactants
(R1 and R2 for bimolecular reactions, R1 = R for unimolecular reactions) and for saddle
point 1 (lowest-energy saddle point) as
Polyrate 124
FR1 =QMS-T,R1
Q1QH, R1
(10)
FR2 =QMS-T,R2
Q1QH, R2
(11)
F‡, 1 =QMS-T,‡
Q1QH, ‡
(12)
Then we obtain the MP-VTST rate constants as
kbimolMP-CVT/MT = g
F‡,1
FR1FR2k
bimol(1), QH-TST
(13)
kunimolMP-CVT/MT = g
F‡,1
FR1k
unimol(1),QH-TST
(14)
10.O.4. FMP-VTST
An FMP-VTST calculation is the same as an MP-VTST one except for the
transmission coefficients. One replaces kkQH and Gk
QH-CVT by kkT and Gk
T-CVT in
equation (8); these quantities are obtained by running SS-T calculations in Polyrate with
the keyword SSTOR. In particular, the recrossing transmission coefficient GkT-CVT is
calculated as
GkT-CVT =
k(k),T-CVT
k(k),T-TST (15)
Polyrate 125
Part III Theory Background for VRC-VTST
11. THEORETICAL BACKGROUND ON VRC-VTST
For an association reaction without a barrier or with a negligible barrier, we recommend
using the multifaceted (MF) extension of variable-reaction-coordinate variational
transition state theory (VRC-VTST) . The references for VRC-VTST is Y. Georgievskii
and S. J. Klippenstein, J. Chem. Phys. 2003, 118, 5442, and the reference for the
extension of VRC-VTST to use MF dividing surfaces is Y. Georgievskii and S. J.
Klippenstein, J. Phys. Chem. A 2003, 107, 9776.
In VRC-VTST, the reaction coordinate and dividing surfaces are defined in a different
way than in RP-VTST. In VRC-VTST, the reaction coordinate s is defined by the
distance between a pivot point on one reactant and that on another, and the dividing
surfaces are defined in terms of pivot points tied to each of the reactants. Choices of the
number and location of these pivot points yield different definitions of the reaction
coordinates and hence of the generalized transition state theory dividing surfaces, and
reactive flux is variationally minimized with respect to both these choices and the
distance between pivot points in the two reactants. The original version of VRC-VTST
employed one pivot point on each reactant, and the MF extension involves two and more
pivot points on one or both reactants. In this manual we consider the use of MF dividing
surfaces to a special case of VRC-VTST. The evaluations of the reactive flux involves
Monte Carlo integration over the coordinate space degrees of freedom of the classical
phase space representation of the generalized transition state partition function for
arbitrary orientations of the reagents over a wide range of interfragment separations.
Because there is no saddle point for a barrierless association reaction, the conventional
TST rate is not calculated. The START section only needs the electronic degeneracy
information for electronic partition function calculations. Association rate constants can
be calculated by CVT, VT, or E,J -VT. Tunneling calculations cannot be performed
for this type of calculation.
11.A. Variable reaction coordinate
When a single-faceted dividing surface is used, the reaction coordinate s for a barrierless
association reaction is defined as the distance between two pivot points, one associated
Polyrate 126
with each of the two reactants. Since s is defined as a distance here, its value is always
positive. Thus, it has a different meaning from the s used in RP-VTST. The following
scheme shows the definition of the reaction coordinate s for the case of a single-faceted
dividing surface.
Here, the two ovals represent the two reactants. COM1 and COM2 are their centers of
mass. P1 and P2 are pivot points associated with reactant 1 and reactant 2, respectively.
d(1) and d(2) are vectors connecting a pivot point with its associated reactant’s center of
mass, respectively. When the distance s between two pivot points is fixed, the directions
of s, d(1), and d(2) are sampled over the whole phase space simultaneously. The lengths
of these vectors are fixed during the sampling over their orientations.
In the VRC-VTST approach, the modes of motion are divided into two sets, conserved
modes and transitional modes. The conserved modes correspond to the vibrational modes
of the two reactants. In the complex of two reactants, these modes usually correspond to
the modes with highest vibrational frequencies. VRC-VTST, at least in its present state of
development, assumes that changes of conserved modes are negligible during the reaction
process. The transitional modes include the other vibrational modes except conserved
modes in the complex and the overall rotations. These modes change from free rotation
and translation at infinite separation of the reactants to vibrational motion and overall
rotation during the reaction process. The new vibrational modes are very floppy and are
best thought of as liberations.
Polyrate 127
The high-pressure limit rate constant for the generalized transition state at location s
along the reaction coordinate and at the temperature T can be expressed as
k(T,s) =2
2pge
s1s2
s‡Q1Q2
2p
mkBT
æ
è ç
ö
ø ÷
3
2dE e-E/kbT dJ N(E,J,s)ò (1)
where s is the value of reaction coordinate, which is defined above as the distance
between two pivot points; ge is the ratio of the electronic partition function of the
transition state to the product of the electronic partition functions of reactants; is the
reduced mass; Q1 and Q2 are the rotational partition functions of the reactants calculated
without symmetry numbers; J is the unitless total angular momentum quantum number;
N(E,J ,s) is the number of accessible states of the generalized transition state s for total
energy E and angular momentum Jħ; and σ1, σ2, and σ‡ are the rotational symmetry
numbers for the reactants and transition state, respectively.
The keyword SIGMAF in RATE section (see Section 13.A.6) is equal to σ1σ2/σ‡. For
reactions in which the two reactants are the same, SIGMAF is 0.5; for reactions in which
the two reactants are different, SIGMAF is 1.0. This is explained in the following
paragraph. As background for this explanation, we first note that eq. (137) in the review
by Bao and Truhlar1 is identical to eq. (4) in the PNAS paper by Bao et al.,2 although in
the PNAS paper we include the rotational symmetry factors in the reactant partition
functions, whereas in eq. (137) of the review we separated them. Note also that σ1 and σ2
should have their correct symmetry numbers as usual.
The next question is: What is σ‡? Georgievskii and Klippenstein3 (in their eq. 2) define
σ = σ1σ2/σ‡
and they make the assumption that – since the transition state is loose – there is free
rotation of both species, such that the transition state partition function contains the
product of the two rotational partition functions. Then
σ‡ = σ1σ2σadd
1 J. L. Bao and D. G. Truhlar, Variational Transition State Theory: Theoretical Framework and Recent Developments, Chem. Soc. Rev., 2017, 46, 7548-7596. doi.org/10.1039/C7CS00602K 2 J. L. Bao, X. Zhang and D. G. Truhlar, Association of CF2 and Dissociation of C2F4 by
Variational Transition State Theory and System-Specific Quantum RRK Theory, Proc. Natl.
Acad. Sci. U. S. A., 2016, 113, 13606. doi.org/10.1073/pnas.1616208113 3 Y. Georgievskii and S. J. Klippenstein, Long-range transition state theory, J. Chem. Phys.,
2005, 122, 194103. doi.org/ 10.1063/1.1899603
Polyrate 128
where σadd is the additional symmetry gained in the transition state. Because we sample
all possible orientations (Euler angles) of the transition state classically in VRP-TST, we
must divide by two when the association reactants are identical because the phase space
may be divided into two quantum mechanically indistinguishable spaces when the two
reactants are identical. This means that σadd equals 1 if the species are different and equals
2 if they are the same. Therefore σ1σ2/σ‡ equals 1 if the species are different and equals
0.5 if they are the same. One could call this the loose-transition-state assumption for the
symmetry number of the transition state.
The number of accessible states for the transitional modes with total energy E and
angular momentum quantum number J can be written as
(2)
where denotes the average over all possible orientations of the two reactants and of
the orientation of the vector s; Q means a specific configuration of the system. Since this
multidimensional integral is carried out by Monte Carlo integration, the configurations of
the system are randomly sampled over the whole phase space corresponding to a given s.
In our implementation, one specific random configuration is determined by the following
procedure:
(1) P1 is always taken as the origin of the system for every random configuration.
(2) The position of P2 is determined by a random solid angle
(3)
where
xP2 is the Cartesian coordinate of pivot point P2; )( 12
1
12 −A is the inverse rotation
matrix,
A12-1 =
cosq12 cosf12 -sinf12 sinq12 cosf12
cosq12 sinf12 cosf12 sinq12 sinf12
-sinq12 0 cosq12
æ
è
ç ç ç
ö
ø
÷ ÷ ÷ (4)
(3) Since the Cartesian coordinates of P1 (
xP1) and P2 (
xP2 ) are known, the Cartesian
coordinates of the center of mass of the kth reactant (
xcomk) are given by
(5)
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(6)
where is the inverse rotation matrix, and is solid angle for the
kth reactant; )(kd is the length of vector )(kd .
(4) Since the internal geometries of the reactants are fixed at the input ones, and their
center of mass positions are determined in step 3, the coordinates of the generalized
transition states are simply obtained by a translation.
The quantity ),,,( sQJEN q can be loosely viewed as number of accessible states for a
specific configuration Q with total energy E and angular momentum Jħ, which can be
expressed as
, (7)
F = 1+ m n(12) ´d(k) ×ni(k)( )
i=1
vk
åk=1
2
å2
/Ii(k) , (8)
where denotes the averaging over all possible orientations of the vector of angular
momentum J while its length is fixed. In equation (7), is a kinematic factor given by
Equation (8);
v equals v1 + v2 + 3 where
vk (k = 1,2) is the dimensionality of the
orientational space for the kth reactant;
Ii(k) denotes the ith moment of inertia of the kth
reactant, and
Ii is the ith moment of inertia for the system as a whole;
n(12)is the unit
vector directed from the second pivot point to the first one;
d(k)is the vector connecting
the center of mass of the kth reactant to its pivot point;
ni(k) is the unit vector directed
along the ith principal axis of the kth reactant;
ka is the number of monatomic reactant,
which should be equal to 0 or 1.
Polyrate 130
Although Equation (8) for the kinematic factor is valid for both linear and nonlinear
molecules, it is convenient to rewrite the term for linear molecule in a different form:
mI-1 (n(12) ´d ×ni
i=1
2
å )2 = mI-1 1- (n(12) ×n0)2[ ], (9)
where 0n is the unit vector directed along the axis of the molecule; I is the moment of
inertia.
There are three ways to perform variational calculations. They correspond to optimizing
the transition state dividing surface using three different ensembles. The resulting rate
constants are labeled canonical variational theory (CVT), microcanonical variational
theory (VT), and energy and total angular momentum resolved microcanonical
variational theory (E,J -VT), respectively. We now discuss these three choices:
(i) Energy and total angular momentum resolved microcanonical variational theory:
For E,J -VT theory, N(E,J ) is minimized with respect to s for each E and J. Then the
integral in Equation (1) is calculated using the optimized N(E,J ).
The minimum of the number of accessible states is obtained by interpolation from a
quadratic fit to N(E,J ,s) at the three values of s nearest to the minimum. We call this
method a 3-point fit; 3-point fits are also used in VT and CVT. The integrals over E and
J for the optimized N(E,J ) in Equation (1) are approximated by Gauss-Laguerre and
Simpson’s rule quadratures, respectively.
(ii) Microcanonical variational theory:
For microcanonical variational theory (VT), the integral over J in Equation (1) is carried
out first to get N(E,s). By integrating Equation (7) over J and substituting the result into
Equation (2), the number of accessible state N(E,s) is obtained as the following
expression:
(10)
Then N(E,s) is minimized with respect to s for each E, and the optimized N(E) is used for
the integral over E.
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(ii) Canonical variational theory:
For canonical variational theory (CVT), N(E,J ,s) is calculated for all E and J at a single
s value. Then the rate constants k(T,s) is minimized with respect to s for each T. The
analytic result of the integral in Equation (1) is expressed as:
(11)
11.B. Multifaceted dividing surface
When one uses single-faceted dividing surfaces, two pivot points (with one on each of the
associating reactants) and a fixed distance between them form a spherical dividing
surface. But in many cases the reactants of association reactions have multiple binding
sites. Multiple binding sites on one or both reactants require more pivot points to increase
the flexibility of the shape of the dividing surface. Let’s assume that n1 pivot points are
assigned to reactant 1 and n2 pivot points are assigned to reactant 2, and the reaction
coordinate value is s. Therefore there are
n1 ´ n2 pairs of pivot points. Each pair of pivot
points corresponds a sphere, and the points on each sphere are selected according to the
following condition to form a composite dividing surface:
mini=1, j=1
n1,n2ri, j = s (12)
where
ri, j is the distance between the ith and jth pivot points associated with the first and
the second reactant, respectively; s is the value of reaction coordinate. The meaning of
Equation (12) is that at one particular configuration of the complex at any of the spheres
formed by the
n1 ´ n2 pairs of pivot points, if the minimum of the distances between
pivot points associated with different reactants equal to the value of reaction coordinate,
this configuration will be accepted in Monte Carlo sampling. Therefore the composite
dividing surface has
n1 ´ n2 elementary surfaces; each of the elementary surfaces is
called a facet, and the composite surface is called a multifaceted (MF) dividing surface.
In variational calculations, various locations of pivot points should be considered to
minimize the reaction rate. Users are responsible to try various sets of locations of pivot
points; that is, Polyrate has not automated this. The optimal locations of pivot points are
the locations that minimize the reaction rate; but the user must be careful that the MF
Polyrate 132
dividing surface defines by the chosen locations of the pivot points separates reactants
from products.
11.C. Overview of program flow for VRC-VTST calculation
When the VRC method is used for loose transition states by turning on the VRC
keyword in the GENERAL section, the program will not use the MEP as the reaction path,
but will instead use variable reaction coordinates and either single-faceted or multifaceted
dividing surfaces. After the MAIN program reads all the information provided at reactants,
subroutine VRCTST is called. Note that user gives the information about two reactants in
this case, and the START section only need the ELEC keyword for electronic degeneracy
information. If only the forward reaction rate constants for association need to be
calculated, the product information is not required. In VRC-VTST calculations, the MAIN
program and subroutine VRCTST are parallelized using MPI, and they work independently
on different processors to read the same fu5 input file and perform Monte Carlo
sampling. During the Monte Carlo sampling, only energies are calculated (for various
geometries along the reaction path), and gradients and Hessians are not required. When
the Monte Carlo sampling is finished on all processors, one processor (rank 0 in MPI) is
used to collect the data calculated on all the processors and to perform the rest of the
calculations to get reaction rate constants.
11.D. Implementation details of the E, J-resolved microcanonical VRC algorithm
This section contains material from the Supporting Information Appendix of ref. [75]
of Sect. 20.
We here describe the implementation details of the E,J-resolved microcanonical
VRC algorithm for the case of two pivot points on fragment 1 and two on fragments 2; the
generalization to a larger number of pivot points is straightforward. We denote the pivot
points on fragment 1 as point 1 and point 2 and the pivot points on fragment 2 as point 3
and point 4. The range of reaction coordinate s searched for a variational transition state is
from sl to su (“l” stands for lower edge of the range, and “u” stands for upper edge of the
range), and the search for a variational transition state is carried out by varying s with increments of size sstep.
We define the vector s as a vector connecting two pivot points, one in each fragment.
This is illustrated in Scheme S1, where we are considering a particular pair of pivot points,
namely pivot point 1 of fragment 1 and pivot point 3 of fragment 2, so we only show the
vector s that connects these two pivot points, and only these two pivot are shown (other
pivot points on fragments 1 and 2 are not shown).
In the computer code, we loop over the pairs of pivot points with one on each
fragment (1-3, 1-4, 2-3, 2-4), and for each pair of pivot points, the vector s is defined as
the vector that connects the pivot point on fragment 1 with the pivot point on fragment 2.
Polyrate 133
The magnitude of s is denoted as s; this is the same as the reaction coordinate s mentioned
in the first paragraph.
Scheme S1
Step 1: Set the length of the reaction coordinate s to sl.
Step 2. Do for m from 1 to 4. For each m, we consider a pair of pivot points with
one on each fragment. Index m =1 corresponds to pair 1-3, m = 2 represents the pivot points
pair 1-4, m = 3 represents the pivot points pair 2-3, m = 4 represents the pivot points pair
2-4. For our explanation we will use m =1 as an example; in particular, m = 1 corresponds
to choosing pivot point 1 and pivot point 3. For case m = 1 or 2, P1 is pivot point 1, and for
m = 3 or 4, P1 is pivot point 2. For the case m = 1 or 3, P3 is pivot point 3; and for m = 2
or 4, P3 is pivot point 4.
Each performance of Step 2C-1 is a Monte Carlo sample. The number of Monte
Carlo samples per value of m is denoted as NMC, which is a number specified by the user,
and which is the same notation as used in the input and the code. That is, for each m, there
are NMC Monte Carlo samples. Because each pair of pivot points determines one facet of
the dividing surface, and we have four pairs (i.e., we have a four-faceted dividing surface),
the total number of Monte Carlo samples is 4NMC. In eq 12 of J. Phys. Chem. A 2003, 107,
9776, which will be used in Step 4, the variable M is equal to 4NMC.
Step 2A for this pair m: Put fragment 1 in a specific initial orientation (this starting
orientation is determined randomly) with respect to P1; set the vector s (as shown in
Scheme S1) in a specific initial direction (this direction is also determined randomly as a
start direction) so that P3 position has been decided; and then put the fragment 2 in a
specific initial orientation (this starting orientation is determined randomly) with respect
to P3. Therefore the coordinates of the whole system and other pivot points are determined.
Calculate the length of the vector RCOM that connects the centers of mass of the fragments.
Step 2B for this pair m: Do for i from (m – 1)NMC + 1 to (m – 1)NMC + NMC.
Starting from the initial configuration determined in Step 2A, we now start doing Monte
Carlo sampling, i.e., randomly orientating the two fragments, while keeping the length of
vector s as specified in Step 1. When orientating the fragments, P1 is always taken as the
origin of the coordinates system. Then, the position of P3 is determined by a random
solid angle. After reorienting s, also reorient fragment 2 (the solid angles for these
Polyrate 134
reorientations are determined randomly). This now yields configuration i.
Step 2C for this i:
Step 2C–1: Fragment 1 has pivot points 1 and 2, and fragment 2 has pivot points 3
and 4, and the distances between each of the various pairs of pivot points (with one on each
fragment) can be computed. Compute the distance rij (where i = 1, 2, and j = 3, 4) for each
pair of pivot points (1-3, 1-4, 2-3, 2-4) for current Monte Carlo sample configuration. If
any of the four rij is greater than or equal to s (no matter which pair of the pivot points
satisfies this condition), then go to Step 2C-2, otherwise abandon this configuration. If this
configuration is abandoned, it does not count in ¢M in eq. 13 of J. Phys. Chem. A 2003,
107, 9776; if this configuration is accepted, then it increases the value of ¢M by 1.
Step 2C–2: For the specific configuration accepted in Step 2C-1, compute the
moment of inertia of each fragment and the unit vector along its principal axis; and
calculate the kinematic factor Φ (eq. 2.40 in J. Chem. Phys. 2003, 118, 5442). Next
compute number of states Nq(E,J,s,i) for this value of the reaction coordinate s and this
specific specific configuration i, and for each combination of total energy E and angular
momentum vector J (the length of which is denoted as J), averaged over all the possible
orientations of vector J while its length is fixed; this is eq 9 of J. Phys. Chem. A 2003, 107,
9776, and it is computed at using eq 2.39 in J. Chem. Phys. 2003, 118, 5442. Note that we
included the correction factor of 2 that is indicated in reference 12 of J. Phys. Chem. A
2003, 107, 9776.
Step 2D: If you have not yet done NMC samples for this m, go back to Step 2B,
except start with the present configuration rather than the initial one. If you have completed
this m, go to step 2E.
End do loop over index i.
Step 2E: If m is less than 4, increment m by 1 and carry out Steps 2A to 2D for the
next pair of pivot points.
End do loop over index m.
Step 3. Now compute the generalized transition state approximation (for a transition
state at reaction coordinate value s) of the number of states for the transitional modes at
total energy E and total angular momentum J. This is given by
NGT E, J, s( ) =1
MNq
i=1
¢M
å E, J, s, i( ) (13)
Step 4: If s < su, increase the length s of vector s by sstep, and go back to Step 1. After
all the values of s specified by the user have been considered, go to Step 5.
Step 5: In E,J-resolved microcanonical variational theory, for each E and J,
minimize N(E,J,s) with respect to s. This yields
NmVT E, J( ) = NGT E, J, s*( ) (14)
where s*
is the value of s that minimizes the number of states. Then plug NmVT E, J( )
into the rate constant expression and evaluate the integral to obtain the final rate constant
k(T).
Polyrate 135
PART IV DESCRITION OF INPUT FILES
12. DESCRIPTION OF INPUT FOR RP-VTST
In the following subsections, a record-by-record description of the data for each input file
that is used for RP-VTST calculations is given:
Subsection 12.A: the input data needed from unit fu5;
Subsection 12.B: the input data needed from unit fu29;
Subsection 12.C: the input data needed from unit fu30;
Subsection 12.D: the input data needed from unit fu31;
Subsection 12.E: the input data needed from unit fu40;
Subsection 12.F: the input data needed from unit fu50;
Subsection 12.G: the input data needed from unit fu51.
12.A. General description of file fu5 input
The input for FORTRAN unit fu5 is of the free format keyword style. The fu5 input
consists of up to twelve sections. These are defined in sub-section 12.A.1. The input file
consists of section headers (section headers are always preceded by a star, *) and
associated keywords.
The keywords are of three types: switch, variable, and list. A switch keyword acts as a
toggle for an option. A switch keyword, for example SWITCHKEY, usually has an
associated form, for example NOSWITCHKEY, that causes the opposite action. A variable
keyword always requires an argument. These are usually used for parameters that have
to have a value, such as step sizes, convergence criteria, etc. The argument must appear
on the same line as the variable keyword. The third type is the list keyword. A list
keyword has one or more level-2 keywords associated with it; these keywords may be
switch or variable keywords, and the latter kind have arguments. The use of a list
keyword takes the form:
LEVEL1KEYWORD
LEVEL2KEYWORDA
LEVEL2KEYWORDB
...
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END
where the END line is mandatory.
All switch and variable keywords have default values, and these types of keywords need
be given only if the user wishes to override the default. Some, but not all, list keywords
have defaults as well. (Additional keywords, called level-2 keywords or subkeywords,
are associated with some list keywords — see above. Sometimes, but not always, level-2
keywords have defaults.) List keywords start a subsection that is always terminated with
an END line.
Except for the input of the TITLE keyword in the GENERAL section, all input is case
insensitive, and anything after a pound sign (#) on a line is assumed to be a comment.
Blank lines are ignored. It is highly recommended that the novice user print out one of
the test run input files and compare it with the descriptions in the following subsections.
A suggested file for this purpose is ch5j2tr3.dat. The rest of subsection 12.A details the
keywords for each of the twelve sections. Please note that every keyword must be used
in its proper section, i.e., between the occurrence of its starred header and the occurrence
of the next starred header (or, for the last section, between the proper starred header and
the end of the file).
Polyrate 137
12.A.1. Section descriptions
The following input sections correspond to the major parts of a RP-VTST rate
calculation. Each section begins with a line giving the section name, preceded by an
“ * ”. An input file can contain all or some of these sections in any order except for a
restart calculation. For a restart calculation, the first section in the file must be the
GENERAL section and the REACT1, REACT2, PROD1, PROD2, WELLR, WELLP, START, and
PATH sections cannot be used. Keywords for each section are discussed further in the rest
of this subsection. For runs using the fu30, fu31, or fu40 electronic structure file input
options, one should not include sections SECOND or OPTIMIZATION.
Section Name Description
*GENERAL general data such as the title and defining the atoms involved
*ENERGETICS options for computing potential energy and first derivatives
*SECOND options for computing second derivatives
*OPTIMIZATION methods for performing geometry optimizations
*REACT1 definition and properties of the first reactant
*REACT2 definition and properties of the second reactant
*PROD1 definition and properties of the first product
*PROD2 definition and properties of the second product
*WELLR definition and properties of the reactant side well
*WELLP definition and properties of the product side well
*START definition and properties of the saddle pt. or starting geom.
*PATH options for computing the MEP
*TUNNEL options for computing the tunneling corrections
*RATE options for computing the reaction rate
Polyrate 138
12.A.2. GENERAL section
The GENERAL section is used to give a title that can be used to identify the run, define all
the atoms in the reacting system, specify the potential energy surface or electronic
structure input option to be used, set up restart criteria (if applicable), and specify
whether IVTST-0, IVTST-1, VTST-IOC, or VTST-ISPE is to be used. (IVTST-0 can
also be specified on file fu50.) If this is a restart run then the first keyword given in this
section must be TITLE. It is good practice to always make this the first keyword so that
input files can be easily identified. The table below lists all the valid keywords for the
GENERAL section. Indented keywords are level-2 keywords, and the others are level-1
keywords. Level-2 keywords are always associated with a level-1 list keyword and must
come after that keyword and before any other level-1 keyword or starred header. In the
alphabetical glossary that follows a more complete explanation for each keyword is
given. In a standard run this section would have the TITLE and ATOMS keywords. Note
that ATOMS is a required keyword.
When using electronic structure input files, IVTST-M is on if and only if one uses file
fu31 or if one sets LOPT(2) = –1 in file fu30 or if one sets MAXLPTS = –1 in file fu40.
Otherwise IVTST-M is off, which means that any interpolation Polyrate needs to
perform to fill the save grid storage arrays is calculated by Lagrangian interpolation.
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Basic:
Keyword Type Default Description
TITLE list blank title with 5 lines maximum
ATOMS list required atoms in system
CHECK switch off check the input data
CLASSVIB switch off classical treatment of vibrations for vibrational partition function
DL variable none interpolated corrections
ICOPT list not used interpolated correction options
BOTH switch off based on corrected and uncorrected data
CORRECT switch on based on corrected data
ENERGY variable seckart Eckart function fit to VMEP(s)
FREQ variable icl interpolated correction of frequency
IVTST0 switch off zero-order IVTST
IVTST1 switch off first-order IVTST
INPUNIT variable angstrom specifies the units in fu5 input file
OUTUNIT variable angstrom specifies the units in fu6 and fu14 output files
MDMOVIE switch off write MDMOVIE input file
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Basic:
Keyword Type Default Description
RESTART list not used restart options
WRITEFU1 switch off write restart file on unit 1
READFU1 switch off read restart file from unit 1
READFU1&2 switch off read restart files from units 1&2
WRITEFU3 switch off read from 1&2, write to 3
MERGE variable 0 an option for merging MEPs
SUPERMOL switch on supermolecule mode for reactants and products
WRITE62 variable none write information in the fu62 file
WRITEFU30 switch off write an fu30 file
WRITEFU31 switch off write an fu31 file
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Glossary of GENERAL keywords
ATOMS
ATOMS is a required list keyword that is used to specify all the atoms in the system. For
each atom the user must specify n, a sequential number unique to each atom in the
molecule, and a label, either the atomic number or symbol of atom n. The mass of the
atom in atomic mass units (amu) can also be specified following the label. If it is not
included then the mass of the most prominent isotope is used. This program uses the
universal atomic mass scale, i.e., the mass of 12C is 12.000000. (For this scale, the
correct abbreviation is u, although most people use the old-fashioned abbreviation amu.)
The mass is supplied from an internally stored table using the atomic number or symbol
as given by the user. Note that the unique number n will be used in other sections to
specify the atom. The example below corresponds to monodeuterated water.
Example: ATOMS
1 O
2 H 1.0078
3 H 2.0140
END
CHECK
CHECK is a switch keyword that tells the program to stop immediately after checking the
input data files. It is especially useful to use this keyword before a long or complicated
calculation to make sure that all the data are input correctly. The default is off.
CLASSVIB (NOCLASSVIB)
CLASSVIB is a switch keyword that determines if the vibrational partition functions are to be calculated assuming a classical treatment of the vibrations. The default is that vibrations are treated as quantized. If CLASSVIB is used, all vibrational partition functions are calculated using the classical expression for harmonic oscillators; therefore, no anharmonicity should be specified for any modes.
Polyrate 142
DL
DL is a variable keyword that determines if the dual-level interpolated corrections are
done. (See Subsection 10.H.) The default is none. See Section 12.F. This keyword can
also be used to perform IVTST-0 calculations with unit fu50; see Section 6.N. The valid
options are
Option Description ioc dual-level using fu50 (VTST-IOC)
ispe dual-level using fu51 (VTST-ISPE)
none dual-level calculation is not performed (default)
Example: DL ioc
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ICOPT
ICOPT is a list keyword that sets options for interpolated optimized corrections. If this
keyword is used, then it is assumed that VTST-IOC is desired, and the DL keyword is set
to ioc. Note that if neither icr nor ica is specified, the correction defaults to the ICL
method, and if energy deckart is not specified then the single Eckart function is
used. (This differs from versions 7.2 – 7.9.2 and earlier) The ICA, ICL, and ICR
schemes, and the two ways to use Eckart functions are discussed in section 10.H. The
valid options are given below.
Option Description Default
both separate calculations will be based on the corrected off
and uncorrected data
correct calculation will be based only on the corrected data on
energy interpolated optimized corrections for energies: seckart
deckart - difference of two Eckart functions fit to
the VMEP(s) curve at higher level and
Eckart function fit to lower level seckart - do not use Eckart function fit to the
VMEP(s) curve at higher level but rather
use a single Eckart fit to the difference
freq interpolated optimized corrections for frequencies: icl
ica - interpolated correction based on arithmetic
differences
icl - interpolated correction based on logarithm of
ratios
icr - interpolated correction based on ratios
none - no corrections
Example: ICOPT
ENERGY DECKART
FREQ ICA
BOTH
END
Polyrate 144
INPUNIT
INPUNIT is a variable keyword that specifies the units for the geometries and distances
given in the fu5 input file. This keyword will have no effect on selecting the units for the
geometries and variables for distances in other input files (units fu29, fu30, fu31, fu40, or
fu50). The default is ang.
Option Description ang angstroms
au atomic units
Example: INPUNIT AU
IVTST0
IVTST1
IVTST0 and IVTST1 are switch keywords to turn on the zero- and first-order Interpolated
VTST (IVTST-0 and IVTST-1) calculations, respectively (See Subsection 6.N.). The
default is off.
MDMOVIE
MDMOVIE is a switch keyword that determines if an input file for MDMOVIE should be
written out. MDMOVIE is a visualization program that allows animation of motion of the
system along the MEP. The default is off.
OUTUNIT
OUTUNIT is a variable keyword that specifies the units for the geometries and distances
given in the fu6 and fu14 output file. The default is ang.
Option Description
ang angstroms
au atomic units
Example: OUTUNIT AU
Polyrate 145
RESTART
RESTART is a list keyword that gives the user control over the restart capability of the run
or designates the current run as a restart calculation. See Section 7.C. for general
comments on this option. If this keyword is not used, a future calculation at a different
temperature must start from scratch. Alternatively a user can use the writefu1 option
within RESTART and the reaction path will be written to unit fu1. In future runs, the user would just need to specify the readfu1 option within RESTART for the same reaction
path to be read from unit fu1. All the valid options are given below. Note that merge
requires an argument specifying the increment value. The default is that this keyword is
not included, i.e. this is not a restart run and no restart file should be written.
Option Definition
writefu1 write restart information to unit fu1 for future use
readfu1 restart calculation using information on unit fu1
readfu1&2 restart calculation using merged MEP, MEP #1 on unit fu1 is
merged with MEP #2 on unit fu2 and the merged file is not
saved.
writefu3 the merged MEP from readfu1&2 is written to unit fu3
merge x increment in s to be added to the s values of MEP #2 when it is
merged with MEP #1. This is required if the READFU1&2 option
is used. The default unit is angstroms and it can also be in bohr
by specifying the keyword INPUNIT AU.
writefu30 write an fu30 file
writefu31 write an fu31 file
Example: RESTART
READFU1
END
NOTE: When writing an fu30 file (writefu30 option) the user needs to supply an
fu30 file with the necessary LOPT(1-40) options.
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SUPERMOL (NOSUPERMOL)
SUPERMOL is a switch keyword which indicates that the supermolecule mode is used for
reactants and products. The default for SUPERMOL in Polyrate is on. This keyword is used
only when the keyword POTENTIAL is set equal to hooks, and the choice has no effect if
there is only one reactant and one product. The use of supermolecule mode is most easily
explained by an example. Consider a bimolecular reaction with reactants A and B. For an
analytical potential energy function or a non-size-extensive electronic structure method, one
would usually calculate the energy of reactants by placing A at a distance of 20–100 ao from
B and calculating the energy of the AB supermolecule. However, for size-extensive methods
like Hartree-Fock and MP2, one would usually prefer to calculate the energies of A and B
separately and add them. The latter requires NOSUPERMOL.
For a bimolecular system, NOSUPERMOL causes Polyrate to calculate the zero of energy as the
sum of the potential energies of the two reactants using two separate calculations in which
each reactant is treated separately. This is not very useful with an analytical potential energy
surface. When NOSUPERMOL is specified, the geometries in REACT1 and REACT2 each contain
less than the full number of atoms. In the case of SUPERMOL, the first reactant is optimized
and its energy is calculated by having the second reactant frozen at a long distance (which is
specified through the definition of the geometries in section REACT2 in file fu5). Then the
second reactant is optimized with the first one already at its equilibrium geometry, but far
away, and the sum of their energies is obtained as the energy of the supermolecule
calculation, i.e., when SUPERMOL is on one does not add the energies from REACT1 and
REACT2 at the end of the calculation. The same considerations apply to PROD1 and PROD2 if
there are two products.
TITLE
TITLE is a list keyword that allows the user to give a title to the run. The user can specify
up to five lines of 80 characters each. Like all list variables, an end must be given at the
end of the TITLE subsection. This must be the first keyword list in the GENERAL section
for a restart calculation.
Example: TITLE
CH3 + H2 —> CH4 + H TEST RUN
ESD/HARMONIC
END
Polyrate 147
WRITE62
WRITE62 is a variable keyword that determines if a subset of the stationary point
information from file fu61 should be printed in fu62 file. The default is none. The valid
options are
Option Description none no information is printed in fu62
viball frequencies (in cm–1) are printed for all stationary points
vibsp frequencies (in cm–1) are printed only for the saddle point
Example: write62 vibsp
WRITEFU30
WRITEFU30 is a switch keyword that determines if an output fu30 file should be written
out. Notice that the points are not in the required ascending order. Therefore the points
in the created fu30 file need to be reordered by the user before using the file. The default
is off.
WRITEFU31
WRUTEFU31 is a switch keyword that determines if an output fu31 file should be written
out. The written file is ready to use with the unit31 option for the POTENTIAL keyword
in the ENERGETICS section of the fu5 input file. The options for writing the fu31 file
cannot be selected. It will always be written in atomic units, and the program will always
write unscaled gradients and packed Hessians in the fu31 file.
Polyrate 148
12.A.3. ENERGETICS section
The ENERGETICS section is used to define the method for computing the potential energy
of the reacting system and the corresponding first derivatives. The table below lists all
the valid keywords for the ENERGETICS section. In the alphabetical glossary that follows
a more complete explanation for each keyword is given.
Keyword Type Default Description
EZERO variable calculate method for determining zero of E
EZUNIT variable a.u. units of zero of energy
POTENTIAL variable hooks type of PES to be used
Polyrate 149
Glossary of ENERGETICS keywords
EZERO
EZERO is a variable keyword specifying how the zero of energy should be determined.
This keyword is discussed briefly in detail in Section 8.B. Polyrate always sets the zero
of energy equal to the energy of the reactants, which is defined to be the sum of the
energies of both reactants for a bimolecular reaction or to be the energy of the single
reactant for a unimolecular reaction. However, the other option is to read in the zero of
energy with option read #. The default is calculate.
Option Definition calculate If calculate is chosen the program will set EZERO to the
value that it calculates for the energy of the reactants.
read # The read # option, where # is the value of the energy of the
reactants in units specified by the EZUNIT keyword, causes the
program to set EZERO to #.
Example: EZERO read 0.1354
Notes:
(1) If the read # option is chosen, the user must ensure that # is the value of the
energy of the reactants in units specified by the EZUNIT keyword.
(2) If the WKB method is used for any of the vibrational modes of reactant 1, then the
read # option must be used. Otherwise the user can choose calculate.
(3) Another possible use of read # would be to allow efficient calculations for
cases where the reactant energy is already known and would be expensive to recalculate.
However Polyrate always calls at least one of the hook routines for the reactants, so this
efficiency must be implemented by the user if desired.
EZUNIT
EZUNIT is a variable keyword specifying the units used for the zero of energy. The
default is a.u. The other valid option is kcal. Note 1 a.u. = 627.5095 kcal/mol. This
keyword must be read before reading the value of the zero of energy with the read #
option for the keyword EZERO, if that option is used.
Option Definition a.u. atomic units (hartrees)
kcal kcal/mol
Example:
EZUNIT kcal
Polyrate 150
EZERO read 100.1354
POTENTIAL
POTENTIAL is a variable keyword that allows the user to specify the source of the potential
energy information for a single-level calculation or for the lower level of a dual-level calculation. In the current version of Polyrate there are five valid options: hooks,
unit29, unit30, unit31, or unit40. The option hooks means that the user is
providing potential information through the hooks. When Polyrate is used as a stand-
alone package, the hooks call SURF and SETUP; this is how one supplies an analytic
potential energy surface (as discussed in Section 8 of this manual). If unit29 is used
the information is read from file fu29 for an IVTST-0 or IVTST-1 calculation. Specification of one of the keywords unit30, unit31, or unit40 means that the
MEP data is to be read from file fu30, fu31, or fu40, respectively. (as discussed in
Sections 9 and 12.C, 12.D, and 12.E of this manual) The fu30 and fu40 options
(unit30 and unit40, respectively) are called the electronic structure input file options
in older versions of POLYRATE.
The default is hooks. Derivative versions of Polyrate will also have various options for
interfacing with electronic structure packages like ACES II, GAUSSIAN, MOPAC, AMSOL,
etc. This may occur through the hooks (modular mode) or in a less general fashion (non-
modular mode), but now electronic structure input can be used with any of the five
choices of POTENTIAL.
Option Definition hooks use the hooks
unit29 read in from electronic structure file fu29
unit30 read in from electronic structure file fu30
unit31 read in from electronic structure file fu31
unit40 read in from electronic structure file fu40
Example: POTENTIAL unit30
Polyrate 151
12.A.4. SECOND section
The SECOND section is used to define the method for computing the Hessian of the
reacting system when the POTENTIAL keyword is set to the hooks option; this section
should not be included if the option selected for POTENTIAL is unit30, unit31, or
unit40. The table below lists all the valid keywords for the SECOND section. In the
alphabetical glossary that follows a more complete explanation for each keyword is
given.
Basic:
Keyword Type Default Description
HESSCAL variable ghook how to calculate Hessians
Second derivative Polyrate methods:
Keyword Type Default Description
Other:
FPRINT switch off print second derivative information
NUMSTEP variable 1 10-4 au step size for 2nd derivatives of V
NUMTYPE variable Central method for computing 2nd deriv.
Polyrate 152
Glossary of SECOND keywords
FPRINT (NOFPRINT)
FPRINT is a switch keyword that is used if the normal mode energies, eigenvectors and
eigenvalues are to be printed following the normal mode analysis in fu6 output file.
Default is NOFPRINT.
HESSCAL
HESSCAL is a variable keyword specifying how to calculate Hessians. The default is
ghook which means Polyrate will calculate the Hessians by finite differences from the
gradients as specified by NUMTYP. Another option is hhook which means the Hessians
are evaluated by calls to the HHOOK subprogram. See Section 8.C.
Option Definition
ghook call GHOOK to get first derivatives, and use central
differences to compute the second derivatives of the
potential. The step size used is given by the NUMSTEP
keyword.
hhook call HHOOK to get second derivatives.
Example: HESSCAL ghook
NUMSTEP
NUMSTEP is a variable keyword giving the step size in unscaled angstrom (default) or in
unscaled bohr (by specifying the keyword INPUNIT AU) for the numerical second
derivative of potential energy function with respect to the unscaled atomic coordinates for
frequency calculations. The default value is 1.0 10-4 bohr.
Example: NUMSTEP 0.00005
Polyrate 153
NUMTYP
NUMTYP is a variable keyword that is used to specify the method for computing the
numerical second derivatives of the potential energy with respect to unscaled atomic
Cartesians if HESSCAL is ghook. See Section 10.C. The default is central. The
allowed options are:
Option Definition central use central differences of analytic first derivatives to compute
the second derivatives of the potential. The step size used is
given by the NUMSTEP keyword.
quadratic use a quadratic fit of the potential to compute the second
derivatives of the potential. The step size used is given by
the NUMSTEP keyword.
fourth use a fourth order polynomial fit to the analytic first
derivatives to compute the second derivatives of the
potential. Step sizes used are NUMSTEP and 2*NUMSTEP.
Example: NUMTYP fourth
Polyrate 154
12.A.5. OPTIMIZATION section
The OPTIMIZATION section is used to specify the method for carrying out geometry
optimizations when the POTENTIAL keyword selection is hooks. This section is not
needed if POTENTIAL is set to unit30, unit31, or unit40. The table below lists all
the valid keywords for the OPTIMIZATION section. In the alphabetical glossary that
follows, a more complete explanation for each keyword is given.
Basic:
Keyword Type Default Description
OPTMIN variable bfgs how to optimize minima
OPTTS variable nr how to optimize transition state
Two optimization routines are available in POLYRATE. The first is quasi-Newton with
BFGS Hessian updates. The alternative is Newton-Raphson with Brent line
minimization, which is called the NR method. For minima (equilibrium structures of
reactants and products), the default optimizer is BFGS. For saddle points (transition
states), the default optimizer is the NR method. See Section 6.E for further details.
Polyrate 155
Polyrate optimization methods:
Keyword Type Default Description
Common:
PRINT switch off print geometrical parameters and
derivatives after each opt step
Other:
DLX2 variable 1 x 10-5 au step size for first derivative of
grad in geometry optimization
EFOPT list off indicate the option for EF
GCOMP variable 1 x 10-5 maximum allowed component of
the gradient for convergence at
the minima
TSGCOMP variable 1 x 10-5 maximum allowed component of
the gradient for convergence at
the saddle point
HREC variable 10 recalculate Hessian every HREC
step for convergence at minima
TSHREC variable 5 recalculate Hessian every TSHREC
step for convergence at saddle
point
NITER variable 50 max number of iterations for opt
RETRY switch off switch to full Newton method if
BFGS optimization fails
SCALE variable 0.2 step size scaling factor in Newton
search
SDSTART switch on(minima
opt)
off(TS opt)
the first optimization step is
steepest-descent
STPTOL variable 1 x 10-5 au “optimization failure” parameter
Polyrate 156
Glossary of OPTIMIZATION keywords
DLX2
DLX2 is a variable keyword used to specify the step size in unscaled angstrom (default) or
in unscaled bohr (by specifying the keyword INPUNIT AU) for calculating the first
derivatives of the gradients of the potential energy function in geometry optimization.
The default value is 1 10-5 ao.
Example: DLX2 0.000012
EFOPT
EFOPT is a list keyword used to specify information for the Eigenvector Following (EF)
algorithm. There are five possible variables that may be specified, namely, RMAX, RMIN,
OMIN, DDMAX, and DDMAXTS. The RMAX and RMIN variables bracket the ratio of the
calculated energy to the predicted energy; the defaults are RMIN = 0 and RMAX = 4. The
OMIN variable is used to indicate the minimum of the overlap in the direction which is
determined by the dot product between the eigenvector and the previous followed
direction; the default is 0.0 for reactants and products and 0.8 for a saddle point. The
DDMAX and DDMAXTS variables are used to set the maximum of the trust radius (in
angstroms); the DDMAX variable is used for the reactants and products, and the DDMAXTS
variable is used for the saddle point. The defaults are DDMAX = 0.5 and DDMAXTS = 0.3.
Example: EFOPT
RMAX 2.0
RMIN 1.2
OMIN 0.2
END
GCOMP
TSGCOMP
GCOMP and TSGCOMP are variable keywords used to specify the convergence criteria for
optimization of minima and transition states, respectively. The optimization is
considered converged if the maximum component of the gradient in atomic units is
smaller than the value specified. The default value is 1 10-5 Eh/ao for both these
keywords. Sometimes, if the saddle point region is very flat, 1 10-5 is not accurate
enough to produce a good reaction path; in such cases we recommend 1 10-7.
Example: GCOMP 0.000001
Polyrate 157
HREC
TSHREC
HREC and TSHREC are variable keywords used to specify how often an accurate Hessian is
to be computed in a BFGS or Newton-Raphson calculation. See Section 6.E for more
details. Notice that if the number specified is equal to 1 in a Newton-Raphson calculation
(nr option for keywords OPTMIN or OPTTS), a full Newton method is used. At a step
when the Hessian is not recalculated accurately, the Hessian is either estimated using the BFGS formula (bfgs option for keywords OPTMIN and OPTTS) or kept frozen (nr option
for keywords OPTMIN and OPTTS). The defaults are HREC equal to 10 and TSHREC equal to
5.
Example: HREC 1
NITER
NITER is a variable keyword used to specify the maximum number of iterations to be used
in optimizing the geometry. The default value is 50.
Example: NITER 75
Polyrate 158
OPTMIN
OPTMIN is a variable keyword that determines how geometries of minima are optimized.
The default is bfgs.
Option Definition
bfgs specifies to use the Broyden-Fletcher-Goldfarb-Shanno Hessian
update method. The Hessian is calculated using the option
specified in HESSCAL in section SECOND at the initial geometry of
the search; at subsequent geometries, the Hessian is estimated
using information about the Hessian at the previously geometry
and the gradient at the previous and current geometry. (When
the search is complete, the Hessian is again calculated by the
method specified in HESSCAL, and this Hessian is used for
frequencies.)
ef specifies to use the Eigenvector Following algorithm.
nr specifies to use the Newton-Raphson algorithm with Brent line
minimization. ohook optimizes the geometry by calling hooks subprogram OHOOK
using options specified in files fu71 through fu74. See Section
8.C.
Example: OPTMIN bfgs
Polyrate 159
OPTTS
OPTTS is a variable keyword that determines how the geometry of the transition state is
optimized. The default is nr.
Option Definition
bfgs specifies to use the Broyden-Fletcher-Goldfarb-Shanno Hessian
update method. The Hessian is calculated using the option
specified in HESSCAL in section SECOND at the initial geometry of
the search; at subsequent geometries, the Hessian is estimated
using information about the Hessian at the previous geometry
and the gradient at the previous and current geometry. (When
the search is complete, the Hessian is again calculated by the
method specified in HESSCAL, and this Hessian is used for
frequencies.)
ef specifies to use the Eigenvector Following algorithm.
nr specifies to use the Newton-Raphson algorithm with Brent line
minimization.. ohook optimizes TS geometry by calling hook subprogram OHOOK
using options specified in file fu75. See Section 8.C.
Example: OPTTS nr
PRINT (NOPRINT)
PRINT is a switch keyword for printing the geometry and the derivatives after each step in
the geometry optimization in fu6 output file. Default is off, i.e., NOPRINT.
RETRY (NORETRY)
RETRY is a switch keyword specifying to switch to full Newton search (HREC = 1, no
linear search) if the optimization stalls (see STPTOL keyword), instead of quitting. Since
this could be quite time consuming, this option has to be used with care. The default is
NORETRY.
Note: the difference between full Newton and quasi-Newton is that full Newton
calculates a full new Hessian at every step whereas quasi-Newton uses an approximate
updated Hessian. In many cases, if the standard search fails it is better to restart the
optimization with a different geometry than to use full Newton.
Polyrate 160
SCALE
SCALE is a variable keyword giving the unitless step size scaling factor in the Newton
search for a stationary point. The default value is 0.2.
Example: SCALE 1.1
SDSTART (NOSDSTART )
SDSTART is a switch keyword that specifies to start the optimization with a steepest-descent
step. This is equivalent to defining the Hessian at the starting point as a unit matrix. This
keyword is meaningful only in minima optimizations where BFGS is specified. This option
proves useful in speeding up convergence of the optimization when the starting point
happens to be outside the quadratic region of the surface around the minimum (the initial
guess geometry is bad). The default is SDSTART.
STPTOL
STPTOL is a variable keyword that specify the conditions for optimization failure. The
default unit is angstrom and can also be bohr by specifying the keyword INPUNIT AU. If
the maximum component of the Newton optimization step is smaller than the value
specified by STPTOL, the optimization is considered stalled since the geometry is not
changing anymore, and the program quits. This could happen if the (estimated) Hessian
used is bad; that in turn probably means that either HREC or SCALE are too large. The
default value is 1 10-5 ao.
Example: STPTOL 0.0001
Polyrate 161
12.A.6. REACT1, REACT2, PROD1, PROD2, WELLR, WELLP, AND START
sections
The REACT1, REACT2, PROD1, PROD2, WELLR, WELLP and START sections all have the
same set of keywords. A separate section is needed for each reactant and product in the
system and for the saddle point or nonstationary starting point. Thus for a system with
one reactant, one product, and a saddle point the user needs to include the REACT1,
PROD1, and START sections in the input file. For simplicity the keywords have been
broken into two categories: basic and anharmonicity. This is only for clarity in the
manual. The keywords in these categories can be used in any order, except for the
STATUS keyword which must be given as the first option line of a section. Also for
simplicity the keywords in each category have been labeled as either required, common,
or other. The required keyword (GEOM) must be included. The keywords labeled
common are those that might be expected to be found reasonably frequently in input files
for typical Polyrate runs. This labeling is only intended as an aid to the novice user.
Again an alphabetical glossary of all the keywords follows the two summary tables.
Notes that START refers to the saddle point if there is one and to the starting point if there
is no saddle point. Also note that the anharmonicity keywords in the START section
control the anharmonicity all along the reaction path since it must be consistent with the
START point.
The first restart option (See Section 7.C) does not use any of these sections, instead it is
controlled by the RESTART keyword in the GENERAL section. However, the second restart
option (See Section 7.C) is controlled by the STATUS keyword of this section. See the
glossary for the definition and proper usage of the STATUS keyword.
Polyrate 162
Basic:
Keyword Type Default Description
Required:
GEOM list required Cartesian coordinates of atoms
Common:
CONSTANT list not used coordinates held constant in opt.
ELEC list
all degen.
= 1
electronic degeneracies
ENERGY variable none energy of the stationary points
EIGENVECTOR list none eigenvector of the saddle point
FREQ switch on perform normal-mode analysis
FREQUNIT variable waven units of the frequencies
HESSIAN list none Hessian of the saddle point
INITGEO variable geom location of input data that specifies initial geometries
STATUS variable 0 status of the stationary point work
SPECIES variable nonlinrp species type (linearity and phase)
VIB list none frequencies of the stationary points
Other:
DIATOM list do not use
Morse
function
treat diatomic as a Morse function
RE variable none Morse equilibrium bond length
BETA variable none Morse range parameter
DE variable none Morse dissociation energy
LINAXIS variable z-axis orientation of a linear molecule
PROJECT switch on project out overall trans. and rot.
Polyrate 163
Anharmonicity:
Keyword Type Default Description
Common:
ANTLR variable 1 10-8 criterion on Morse xe
DEMIN variable 0.159 lowest dissociation energy (D)
DQQP variable 0.0001 au,
0.001 au
two distances for quad.- quar. fit
HARMONIC switch on all modes harmonic
MORSE switch off all modes Morse
MORSEQQ switch off all modes Morse/quadratic–quartic
MORMODEL variable morsei Morse options
PRMODE switch off print XMOL movie clips
QQWKB switch off WKB with a quadratic-quartic fit
QQSEMI switch off semi-classical WKB with a quadratic-quartic fit to potential
TOR list not used information for modes treated as torsions
TOROPT list not used more information for modes treated as torsions
VANHAR list not used each mode is treated individually
VRANGE list not used each mode is treated individually for a given range of s
WKB list not used WKB with true potential
WKBTOL variable 1 10-8 tolerance for finding eigenvalues
KBQUAD variable 40 no. of quad. points in phase integrals
KBPRINT switch off print turning points
Polyrate 164
Glossary of REACT1, REACT2, PROD1, PROD2, WELLR, WELLP, and START keywords
ANTLR
ANTLR is a variable keyword whose argument is the criterion on the unitless Morse
anharmonicity parameter, xe, such that the quadratic-quartic model is used if xe < ANTLR.
The antlr keyword is only used with the morseqq method. The default value is 1
10-8.
Example: ANTLR 0.000013
CONSTANT
CONSTANT is a list keyword used to specify which of the Cartesian coordinates should be
held constant during the Newton search to find the species' equilibrium geometry. In this
list the unique atom number is used along with x, y, and/or z for those coordinates to be
held constant. The default is that all coordinates are optimized. In most cases the user
needs to specify at least six Cartesians coordinates to be constant for a nonlinear species
and five for a linear species. Note that if this keyword is specified, the default is erased,
and the user should input all the coordinates which are to be held constant.
Example: CONSTANT
1 X Y Z
2 Y Z
3 Z
END
DEMIN
DEMIN is a variable keyword used to input the lowest reactant or product dissociation
energy in a.u., measured from the reactant limit. This is called D in published papers. It
is needed for any of the Morse anharmonicity options and for VT calculations. There is
a default value of 0.159 Eh (= 100 kcal/mol) for this variable but it is dangerous to use
the default. The user is strongly encouraged to understand D if Morse anharmonicity is
used.
Example: DEMIN 0.1733
Polyrate 165
DIATOM
DIATOM is a list keyword that is used if the particular reactant or product is a diatomic
molecule and is to be treated as a Morse oscillator. The default is to treat diatomics by
the same methods as any other kind of molecule; thus this keyword would not be used.
Note that if the DIATOM option is chosen, then the user must specify all three options, Re,
and De, which are the Morse parameters for equilibrium geometry, dissociation
energy, and range parameter, respectively. and De are in atomic units and Re is in
angstrom by default and also can be in bohr by specifying the keyword INPUNIT AU. There are no defaults for these options. The example below corresponds to the O2
molecule.
Example: DIATOM
RE 2.3158
BETA 1.4694
DE 0.1779
END
DQQP
DQQP is a variable keyword with two arguments, which are respectively the first and
second step sizes used when fitting the quadratic-quartic potential to two points along the
normal coordinate. It is in angstrom by default and also can be in bohr by specifying the
keyword INPUNIT AU. Note that the first argument (the first step size) must be less than
the second. DQQP is to be used only if one of the keywords QQWKB or QQSEMI is
specified. Default is 1 10-4 ao and 1 10-3 ao.
Example: DQQP 0.03 1.2
Polyrate 166
EIGENVECTOR
This keyword should be used only in a START section and it should be used if and only if
the STATUS option is equal to 6. EIGENVECTOR is a list keyword that is used to specify the
eigenvectors of the saddle point in an unscaled Cartesian coordinate system. The
eigenvectors of the stationary point should be given in full matrix form with the columns
being a particular mode. In addition, the axes must be consistent with the geometry in
GEOM.
Example: EIGENVECTOR
L11 L21 L31 L41 L51 L61
L12 L22 L32 L42 L52 L62
L13 L23 L33 L43 L53 L63
L14 L24 L34 L44 L54 L64
L15 L25 L35 L45 L55 L65
L16 L26 L36 L46 L56 L66
END
Explanation of example:
Lij is the jth component of the ith eigenvector. Note that j = 1 is for the x
component of atom 1, j = 2 is for the y component of atom 1, j = 3 is for the z
component of atom 1, j = 4 is for the x component of atom 2, etc. Note also that
the eigenvalues must be in reverse canonical order (this order is described in Sect.
6.E). Thus, I=1 is for the imaginary-frequency normal mode, then come the
eigenvectors corresponding to translations and rotations, and finally come the true
vibrations, in order of increasing frequency.
ELEC
ELEC is a list keyword used to specify the degeneracy and energy in atomic units of each
electronic state of this species. Up to three states are allowed. The ground state should
be given first. The default is for all three states to be singly degenerate. The example
given below is for the 3P multiplet of an oxygen atom.
Example: ELEC
5 0.00000000
3 0.00072218
1 0.00103201
END
Polyrate 167
ENERGY
This keyword should be used if and only if STATUS 4. ENERGY is a variable keyword
that is used to specify the energies (a.u.) of a reactant, product, or saddle point.
Example: ENERGY -2.4221970828E-02
FREQ (NOFREQ)
The FREQ keyword is used to specify whether normal mode analysis is carried out. The
default is FREQ.
FREQUNIT
The FREQUNIT keyword is used to specify the units of the frequencies read by the FREQ
keyword. The default is au.
Option Definition
waven Frequencies are given in cm−1.
au Frequencies are given in atomic units.
GEOM
GEOM is a list keyword that is required for all calculations except those with the readfu1
or readfu1&2 option selected for RESTART in the GENERAL section. In this list the
Cartesian coordinates of all atoms in this particular reactant, product or reaction path
species must be given along with each unique atom number. If STATUS (see below) is 0,
the user should choose a geometry that is a guess to the species' stationary-point
geometry. IF status is 2, then the geometry should be the correct geometry, not just a
guess. (See the ATOMS keyword in the GENERAL section for the definition of the unique
atom number. This number must be consistent for each atom in ATOMS and GEOM.) For a
linear species, the user must specify a linear geometry. The example below is for the
same deuterated water molecule used in the ATOMS example. It is in angstrom by default
and also can be in bohr by specifying the keyword INPUNIT AU (not mass-scaled).
Example: GEOM
1 0.000000 0.000000 0.000000
2 -0.241497 -0.945827 0.000000
3 0.956805 0.000000 0.000000
END
Polyrate 168
HESSIAN
If the option of the STATUS keyword is 4, the Hessian of the saddle point should be read
in as a triangular form in unscaled Cartesians. HESSIAN is a list keyword that is used to
indicate the Hessian (hartrees per square bohr) of the saddle point. This keyword is only
valid for the START section, and can not be used in the REACT1, REACT2, PROD1, and
PROD2 sections. In addition, the axes must be consistent with the geometry given in
GEOM. The format is free format, with any number of entries per line and entries on the
same line separated by one or more spaces. Since the Hessian should be a symmetric
matrix we read only the lower triangular part.
Example: HESSIAN
F11 F21 F22 F31 F32 F33
F41 F42 F43 F44 F51 F52
F53 F54 F55 F61 F62 F63
F64 F65 F66
END
Explanation of the example:
The element Fjj’ of the Hessian matrix F corresponds to the same order of
components as explained for j under the EIGENVECTOR keyword.
HARMONIC
HARMONIC is a switch keyword that is used when one wishes to treat all vibrational
modes harmonically. It is the default; i.e., if no keyword is given for anharmonicity then
the harmonic approximation is used. The default is that harmonic is on, so when it is
specified, the purpose is just for clarity (i.e., to make the default explicit).
INITGEO
INITGEO is a variable keyword that is used to indicate the location of the input data that
specifies the initial reactant 1, reactant 2, product 1, product 2, and starting geometries.
The default is geom. The valid options are:
Option Definition geom the initial geometries are taken from the lists following the GEOM
keywords in the react1, react2, prod1, prod2, and start sections of
the fu5 input file.
hooks the initial geometries are taken from the external input files fu71-
fu78.
Polyrate 169
Example: INITGEO geom
LINAXIS
LINAXIS is a variable keyword that is used to indicate the orientation of a linear reactant,
product, or starting molecule. The default is that LINAXIS is off if the initial geometry is
nonlinear and that it is on if the initial geometry is linear. If LINAXIS is on, but no option is specified, the default value is z-axis. The valid options are:
Option Definition
x-axis the linear molecule is aligned with the x-axis
y-axis the linear molecule is aligned with the y-axis
z-axis the linear molecule is aligned with the z-axis
MORMODEL
MORMODEL is a variable keyword that is used to specify which Morse model is to be
used. This keyword is used only if the MORSE or MORSEQQ switch is on. The default is
morsei. Note that the value of DEMIN is specified by the user using the keyword
DEMIN. All the valid options are given below (see Ref. 1 in Sec. 21 for explanations of
these models):
Option Definition
morsei Morse I: VMEP + local D = DEMIN
morseii Morse II: local D from V'''
morseiii Morse III: Morse II if (VMEP + local D) > DEMIN; otherwise
Morse I
morseia Morse Ia: like Morse I except use hyperradius to determine
side of MEP on which concave-side turning point is to be
found if SCT or LCT tunneling correction is done. morseiiia Morse IIIa: like Morse III except replace Morse I by Morse
Ia, i.e., find direction of concave side from hyperradius when
using Morse I and find it using 3rd derivative when using
Morse II
Example: MORMODEL morseiii
MORSE
MORSE is a switch keyword that is used if all vibrational modes are to be treated using the
Morse approximation with the same value of MORMODEL. If this option is chosen, then
the Morse model is specified by the keyword MORMODEL. Default is off.
Polyrate 170
MORSEQQ
MORSEQQ is a switch keyword that is used if all vibrational modes are to be treated using
Morse/quadratic-quartic approximation with the same value of MORMODEL. This means
that the Morse model is used for modes with Morse anharmonicity parameter xe ANTLR,
and the quadratic-quartic option based on second and fourth derivatives of the potential
along the generalized normal mode is used for modes with xe < ANTLR. If this option is
chosen, then the Morse model is specified by the keyword MORMODEL. Default is off.
PRMODE
PRMODE is a switch keyword used to print movie clips of the vibrational modes for the
XMOL program in XYZ format. The file name of a movie clip consists of two parts. The
first part has 4 letters which is used to indicate the type of the species: R1MD for reactant
1, R2MD for reactant 2, P1MD for product 1, P2MD for product 2, RWMD for reactant
well, PWMD for product well, or TSMD for the saddle point. And the second part has a
three-digit integer which is used to indicate the index of the vibrational mode in
decreasing order. Therefore, the maximum number of vibration modes for which this
keyword can be used is 999. Currently, each clip has 20 frames.
PROJECT (NOPROJECT)
PROJECT is a switch keyword that tells the program to use projection operators to remove
overall translations and rotations from the second derivatives at the stationary points.
This projection is not optional along the reaction path, but is optional at stationary points.
Even at stationary points, one obtains more stable numerical results if projection is
applied. The default is PROJECT.
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QQSEMI
QQSEMI is a switch keyword that is used if all vibrational modes are to be treated by using
a quadratic-quartic fit to the potential at two distances (specified by the DQQP keyword)
along the generalized normal mode with the uniform semiclassical WKB method for
computing energy levels. See Section 10.B.1. Default is off.
QQWKB
QQWKB is a switch keyword that is used if all vibrational modes are to be treated using
the WKB method with a quadratic-quartic fit to the potential. The fit is done at two
distances, specified by the DQQP keyword, along the generalized normal mode with the
primitive WKB method for computing energy levels. See Section 10.B.1. Default is off. SPECIES SPECIES is a variable keyword that is used to specify the linearity and phase of the reactant, product, or starting species. See Section 6.B for discussion. The default is nonlinrp. The valid options are given below.
Option Definition
atomic species is a single atom
linrp species is a linear reactant or product
nonlinrp species is a nonlinear reactant or product
ssrp species is a solid-state reactant or product
lints species is a linear transition state or generalized transition state
nonlints species is a nonlinear transition state or generalized transition state
ssts species is a solid-state transition state or generalized transition
state
Example: SPECIES linrp
STATUS
STATUS is a variable keyword that is used to indicate the status of the stationary points.
When the STATUS keyword is used it must be given as the first option line of the
*REACT1, *REACT2, *PROD1, *PROD2, *WELLR, *WELLP, or *START section in which the
keyword is used. The options are:
Polyrate 172
option *REACT1, *REACT2, *PROD1, *PROD2,
*WELLR, or *WELLP *START
0 calculate geometry, energy, and
frequencies
calculate geometry, energy,
frequencies, and eigenvectors
2 read in geometry;
calculate energy and frequencies
read in geometry;
calculate energy, frequencies, and
eigenvectors
4 not available read in geometry, energy and Hessian;
calculate frequencies and eigenvectors
6 read in geometry, energy, and
frequencies
read in geometry, energy, frequencies,
and eigenvectors*
* Note: if cubic is chosen as the value of the FIRSTEP keyword in the PATH section, then
option 6 is not valid.
Note that in the START section if STATUS is 4, then the ENERGY and HESSIAN lists must be
given and if STATUS is 6, then the ENERGY, FREQ, and EIGENVECTOR lists must be given.
The GEOM keyword is always required.
Example: STATUS 2
TOR
TOR is a list keyword that is used to specify the information needed for torsional modes
that will be treated using the hindered-internal-rotator approximation. Note that the MS-
T method is not included in this keyword list, but MS-T can be specified in the PATH
section using the SSTOR keyword. The hindered internal rotator approximation is only
used for a subset of the modes, and this keyword is used to give the parameters for each
of those modes. The user must also use the VANHAR or VRANGE (for generalized
transition states) keyword to specify which mode or modes are to be treated as hindered
internal rotation. There should be one line in the TOR list for every mode treated as a
hindered rotor. There are no defaults. If VANHAR or VRANGE specifies that a mode is to
be treated as a hindered rotor, the line for that mode must be present in the TOR list.
The SRPG is the recommended method when using the TOR keyword. Other methods may
be appropriate for certain systems, but careful analysis should accompany any other
choice. See Ref. 52 and 62 of Sect. 21 for a study and comparison of torsion methods.
Polyrate 173
The input required for each hindered rotator mode is:
MODE P M METHOD N
where
MODE = mode number m
P = number P of distinct minima along the torsional coordinate
M = number M of total minima along the torsional coordinate (M P)
METHOD = one of six methods defined in Section 10.3:
CT Chuang-Truhlar interpolatory method
RPG Torsional Pitzer-Gwinn method
SRPG Segmented Torsional Pitzer-Gwinn method
AS Ayala-Schlegel method
SAS Segmented Ayala-Schlegel method
FR Free Rotor
N = number N of atoms in first subgroup
The user needs to be cautious with the definition of number of distinct minima along the
torsional coordinate. For example, H2O2 has two minima that have the same energy and
frequencies, but they are mirror images of one another, and one cannot be superimposed
to the other. Therefore they are distinguishable. The total symmetry number is the ratio of
M/P, which should not be a non-integer number. Here are a few examples for the values
of P and M.
Molecule P M
CH3-CH3 1 3
ClCH2-CH3 1 3
HO-OH 2 2
ClCH2-CH2Cl 3 3
ClCH2-CH2 3 6
Among the six methods for torsional treatment, SRPG is recommended. Note each
method requires a different set of keywords. For more input information see the
TOROPT section below.
Example: TOR
10 1 3 SRPG 4
END
TOROPT
TOROPT is a list keyword that must be given for modes treated as hindered rotors . Each
record of TOROPT is a single line of the form:
MODE DATATYPE list of values
An END line signifies the end of all records in the list.
Polyrate 174
Which quantities may appear in the list of values depends on DATATYPE. The allowed
values for DATATYPE and the associated lists are as follows:
DATATYPE list
ISB 1i , 2i , …, Ni (the indices of the atoms in the first
subgroup)
NBOND indices of the two atoms that define the rotation axis
(used only when the curvilinear option is used to
calculate the moment(s) of inertia)
CTSCHEME OW/RO/CO/RW/CW/RWO/CWO (one of seven
schemes defined in Ref. 52 of Sect. 21 for CT
method)
CTLEVEL FULL/SF/SC (one of three levels for CT
method)
OMEGA 2w , …, Pw (the frequencies in cm-1)
U 2U , 3U , …, PU (excitation energies in cm-1)
I 2I , 3I , …, PI (moments of inertia in mea02)
READI
I1 (moment of inertia in mea02)
W 1W , 2W , …, PW (barrier heights in cm-1)
WL
WL1,
WL2, …,
WLP (
WL j is the barrier
height from
the minimum j to the maximum on its left in cm-1)
WR
WR1,
WR2, …,
WRP (
WR j is the barrier
height from
the minimum j to the maximum on its right in cm-1)
RATIOL RL1, RL2, …, RLp (RLj is the torsional angle
difference between the minimum j and the maximum
on its left in degrees)
RATIOR RR1, RR2, …, RRp (RRj is the torsional
angle
difference between the minimum j and the maximum
on its right in degree)
The methods specified in the TOR section need different DATATYPE values and the
associated lists. Note that ISB and NBOND are always required except when
CTSCHEME = OW or READI is used. An explanation of DATATYPE requirement for
each method is given below
1. The RPG and AS methods require the following DATATYPE values:
ISB, NBOND, I, WL, and WR
Polyrate 175
In these methods the moment of inertia of the torsional motion I1 is calculated by
the curvilinear model using the input geometry in fu5 file, and the others are given
by the user. The user can run jobs to obtain I2, …, Ip using the corresponding
geometries. The barrier height used in the RPG and AS methods is taken as the
average of the input WL and WR values. The frequency of the lowest minimum is
used.
2. The SRPG and SAS methods require the following DATATYPE values:
ISB, NBOND, I, U, WL, WR, RATIOL, and RATIOR
The SPRG and SAS methods need the same information as their corresponding
non-segmented counterparts except that U, RATIOL and RATIOR are also
required.
3. The FR method require the following DATATYPE values:
ISB, NBOND, and I
4. The CT method requires the following DATATYEP values:
ISB, NBOND, CTSCHEME, CTLEVEL, OMEGA, U, and I.
CTSCHEME list is one of the seven schemes defined in Ref. 52 of Sect. 21:
OW Scheme W
RO Scheme R
CO Scheme C
RW Scheme RW
CW Scheme CW
RWO Calculate I with the R-scheme, read in W, obtain from normal mode or
generalized normal-mode analysis
CWO Calculate I with the C-scheme, read in W, obtain from normal mode or
generalized normal-mode analysis (default)
CTLEVEL list is one of the three approximation levels used for CT method defined
in Ref. 52 of Sect. 21:
FULL full (default)
SF single-frequency
SFE single-frequency and single-energy
Note that the SFE method treats the P minima using the same I, , and W as the input geometry in fu5 file and do count the contributions of the P minima to the
partition function. The single-conformer (SC) method defined in Ref. 52 of Sect. 21
is a special case of SFE method when P equals 1.
Polyrate 176
In the seven distinct schemes, R represents using the rectilinear model to calculate
the reduced moments of inertia of the torsional motion (see refs. 24, 29, and 30 in
Sect. 21 for detailed description of the rectilinear model), and C represents using the
curvilinear model to calculate the reduced moments of inertia of the torsional
motion (Ref. 59 in Sect. 22 gives a detailed description of the curvilinear model).
Compared with the rectilinear model, for which one only needs to indicate which
atoms are in each of the two fragments of the hindered rotation, the curvilinear
model requires this information and also a choice of internal rotation axis (by using
the NBOND keyword) and an assignment (by using the ISB keyword) of the lighter
fragment as the rotational top. The first five schemes use the relationship given by
Eq. (12) of Ref. 52 in Sect. 21 to calculated either I, W, or from the other two.
The RWO and CWO schemes require I, W, and , and use these variables in the
equations of Ref. 52 in Sect. 21 without forcing a relationship between them.
If CTSCHEME = CO or C, then the sum of the masses of the atoms in ISB must be
less than or equal to the sum of the masses of the atoms not in ISB. Note that the
values of P and N that appear in these definitions are specified using the TOR
keyword. In the current version of POLYRATE, the values of OMEGA, U, and W are
assumed to be independent of the value of the reaction coordinate s. That is, only
values for the stationary points can be read in, and for the non-stationary points
along the reaction path, the only hindered rotor parameters that can depend on s are
the value of 1, which is obtained directly from generalized normal mode analysis
if the OW, RO, or CO scheme is used, and from the moments of inertia of the
lowest minimum along the torsion mode, which are computed from the geometry if
the CO or CW scheme is used and from the geometry and normal mode eigenvector
if the RO or RW schemes is used.
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The set of data types expected in the TOROPT list for CT method depend on the
choices of CTSCHEME and CTLEVEL and the number of distinguishable
minima P. In particular, the expected records are:
Choices in DATATYPES expected in TOROPT
P CTLEVEL CTSCHEME Other expected DATATYPES
1 any OW W ( 1W only)
1 any RO ISB
1 any CO ISB, NBOND
1 any RW ISB, NBOND, W ( 1W only)
1 any CW ISB, NBOND, W ( 1W only)
>1 FULL OW U, OMEGA, W
>1 FULL RO ISB, OMEGA, U, I,
>1 FULL CO ISB, NBOND, OMEGA, U, I,
>1 FULL RW ISB, U, I, W
>1 FULL CW ISB, NBOND, U, I, W
>1 SF OW U, W
>1 SF RO ISB, U, I
>1 SF CO ISB, NBOND, U, I
>1 SF RW ISB, U, I, W ( 1W only)
>1 SF CW ISB, NBOND, U, I, W ( 1W only)
>1 SC OW W ( 1W only)
>1 SC RO ISB
>1 SC CO ISB, NBOND
>1 SC RW ISB, W ( 1W only)
>1 SC CW ISB, NBOND, W ( 1W only)
If values are not expected but are given anyway, then these values will be ignored.
The program will not check the correspondence of the TOR and TOROPT keyword
options; it is users’ responsibility to check if the calculation is meaningful. The
defaults are jw = frequency obtained from normal mode analysis at point on
reaction path (j = 1, 2, …, P), jW = 1000 cm-1 (j = 1, 2, …, P), jU = 0, ISBN =
{1 2 3 4}, and NBOND = {4 5}.
The READI option is used to read in the moment of inertia for the initial configuration.
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Example for using CT method with OW and FULL options: TOR
17 2 2 CT 4
END
TOROPT
17 CTLEVEL FULL
17 CTSCHEME OW
17 U 1000.
17 ISB 1 2 3 4
17 OMEGA 110.
END
Example for using CT method with CW and SC options:
TOR
18 1 1 CT 3
END
TOROPT
18 CTLEVEL SC
18 CTSCHEME CW
18 ISB 3 4 5
18 NBOND 2 6
18 W 1450.0
END
Example for using SRPG method:
TOR
6 2 2 SRPG 2
END
TOROPT
6 ISB 1 4
6 NBOND 1 2
6 WL 2545.505 376.905
6 WR 376.905 2545.505
6 RATIOL 112.504 67.496
6 RATIOR 67.496 112.504
VANHAR
VANHAR is a list keyword that is used to specify variable anharmonicity, i.e., that each
vibrational mode is to be treated differently. The default are that all modes be treated
harmonically. This keyword is used to specify those modes that are to be treated
anharmonically. The valid choices are harmonic, morse, morseqq, qqwkb,
qqsemi, and tor. (Note that modes for which the harmonic option is wanted need not
Polyrate 179
be included in the list since it is the default.) Note that for each of these anharmonicity
options there may be other variables that have to be set, and in each case there is keyword
with the same name as the choices just given, i.e., harmonic, morse, morseqq, qqwkb,
qqsemi, and tor. In specifying the modes, note that they are always numbered in order of
decreasing frequency, regardless of symmetry, and that degenerate modes get two
numbers.
The input required is:
mode anharmonicity method
Example: VANHAR
3 tor
5 qqsemi
END
VIB
If the option of the STATUS keyword is 6, frequencies of the stationary point should be
read. VIB is a list keyword that is used to specify the frequencies (a.u. or cm−1 as
determined by FREQUNIT) of a reactant, product, or saddle point. The number of
frequencies to be read is always F, where F is 3N − 6 for nonlinear stationary points, 3N
− 5 for linear stationary points, and 3N for solid-state stationary points. For reactants and
products there should be F real frequencies, and they should be given in decreasing order
of their magnitude. For saddle points, the F − 1 real frequencies should be given first in
decreasing order followed by the imaginary frequency given last as a negative number.
Example: VIB
1.72881D-02 1.72881D-02 1.62501D-02 8.24925D-03
8.07930D-03 8.07884D-03 7.06232D-03 7.06187D-03
6.58527D-03 3.28102D-03 3.28102D-03 -1.24729D-02
END
Polyrate 180
VRANGE
VRANGE is a list keyword similar to VANHAR except that a range of s values can also be
specified for each mode. This means that except for the given modes and their respective
ranges of s, each mode will be treated harmonically. Again the valid anharmonicity
choices are: harmonic, morse, morseqq, qqwk, qqsemi, and tor. Note that for
each of these anharmonicity options there may be other variables that have to be set. For
more information, please see the keyword glossary entry for each method. This keyword
should only be used in the START section. The default unit of s is angstrom and can also
be bohr by specifying the keyword INPUNIT AU.
The input required is:
smin smax mode number anharmonicity
The example below shows the VRANGE input if one wanted to use the Morse I
approximation in the regions 0.01 s 0.5 and –0.15 s -0.01 for mode #2 and the
harmonic approximation everywhere else.
Example: VRANGE
-0.15 -0.01 2 morsei
0.01 0.50 2 morsei
END
WKB
WKB is a list keyword that is used if the zero point eigenvalues are to be computed using
the WKB method with the true potential. See Sections 10.B and 12.B.2. The WKB
keyword applies only to the ground state; another anharmonicity method must be chosen
for the excited states, or else the excited states will be calculated harmonically. The
options in this list control the WKB calculation. They are defined as follows:
Option Description Default
wkbtol tolerance for finding WKB eigenvalues in hartrees 110-8
kbquad number of quadrature points used in calculating WKB 40
phase integrals
kbprint switch for printing values of turning points off
Example: WKB
wkbtol 0.0000002
kbquad 30
kbprint
END
Polyrate 181
12.A.7. PATH section
The PATH section contains the keywords that control the calculation of the reaction path
and the properties along the path. This section is not used in a restart calculation. For
simplicity the keywords have been broken into five categories: basic, integrators, step
sizes for the MEP, extrapolation, and print. This is only for clarity in the manual. The
keywords in any of these five categories can be used in any order. Also for simplicity the
keywords in each category have been labeled as either common or other. The keywords
labeled common are those that might be expected to be found reasonably frequently in
input files for typical Polyrate runs. This labeling is only intended as an aid to the novice
user. Again an alphabetical glossary of all the keywords follows the five summary tables.
If only a conventional transition state theory rate constant calculation is desired, one
needs to include this section only if the Hessians are input in mass-scaled coordinates and
SCALEMASS does not equal 1.0 amu.
Polyrate 182
Basic:
Keyword Type Default Description
Common:
CARTRP Switch on Whether the normal mode analysis for reactants and products is carried out in Cartesian coordinate
COORD
Variable
cart
type of coordinate system to be used for computing vibrational frequencies and generalized normal modes along the MEP
IDIRECT Variable 1 initial direction off of saddle pt.
INTDEF List not used define curvilinear internal coordinates
NSTEPS Variable 99999 max no. of steps along MEP
SADDLE Switch yes whether the reaction has a saddle point
SCALEMASS Variable 1.0 mass-scaled coordinates scale factor
SIGN Variable reactant direction of unbound eigenvector
SRANGE List not used range of s for MEP
SLP Variable +1.0 au upper limit on s before it is extended by interpolation
SLM Variable –1.0 au lower limit on s before it is extended by interpolation
Others:
CURV Variable dgrad method for computing curvature
DLX3 Variable 1 10-4 au step size for 3rd derivatives of PES
FCSCALE List not used the force constant scaling factors for specified internal coordinate
FREQINCR Variable not used Increase low frequencies to a certain number that is as the value of this keyword
FIRSTSTEP Variable nmode method for first step
Polyrate 183
Basic:
Polyrate 184
Keyword Type Default Description
Others:
FREQSCALE Variable 1 Scale factor for frequencies
HESS Switch on Compute the Hessian along MEP
INTMU Variable 1 Number of points on each side of the saddle point for interpolation of eff(s)
ISWR Variable Not used mode index of the reactant frequency which is to be scaled
ISWP Variable not used mode index of the product frequency which is to be scaled
IVTSTMOPT List not used IVTST-M options
LBEXP Variable 3 mapping for curvature components
POLYS switch on include 10 extra points for spline fitting
SINCW variable 0.01 au step size for 10 extra points
TENSION variable -1.0 tension for spline under tension
IVTST0FREQ list not used modifies the frequency of a specified mode along the reaction path
NEXTPT switch off only compute next point on MEP
REORDER switch
off order frequencies along MEP by overlaps
SCALERP switch
off scales frequencies in VIB section if turned on
SCLPT switch
off whether scale the potential if FCSCLAE
is used
SPECSTOP List not used special stop for MEP
CURVE Variable vag the curve on which the check for the special stop is made
Polyrate 185
POINT Variable savegrid the grid on which the end point for the special stop is chosen
PERCENTDOWN Variable 50. the percentage down from the saddle point for the special stop
SSPECIAL list
no special
s val.
special s values for N.M. analysis
SYMMETRY switch off symmetric reaction path
VSCALE variable 1 scale factor for MEP
Polyrate 186
Integrators:
Keyword Type Default Description
Common:
ES1OPT list not used Euler with stabilization
DELTA2 variable 5 10-5 au step size 2 for stabilization
DIFFD variable 1 10-8 magnitude of difference vector
RPM variable ESD reaction path following method
Others:
RODS switch off re-orient the dividing surface
Step sizes for the MEP:
Keyword Type Default Description
Common:
SSTEP variable 5 10-4 au step size for computing MEP
Others:
INH variable 9 ratio of gradients to Hessians
INI variable 1 interval of gradient interpolation step
SFIRST list not used special step size for first n steps
NFSTEP variable 0 number of initial special steps
FSIZE variable 1 10-5 au step size for the special steps
Polyrate 187
Reaction coordinate for the VRC:
Keyword Type Default Description
Common:
SVRC list not used Reaction coordinate setting for
reaction path in variable reaction
coordinate algorithm for loose
transition state
Polyrate 188
Extrapolation:
Keyword Type Default Description
Others:
EXFIRST list not used extrapolate first direction from saddle point.
EXNSTEP variable 0 number of steps
EXREACT switch off extrapolation is towards reactants
EXPROD switch on extrapolation is towards products
EXSTEP variable 0.03 au step size
EXALPHA variable 1.0 extrapolation range parameter
EXSECOND list not used extrapolate second direction from
saddle point
EXNSTEP variable 0 number of steps
EXREACT switch on extrapolation is towards reactants
EXPROD switch off extrapolation is towards products
EXSTEP variable 0.03 au step size
EXALPHA variable 1.0 extrapolation range parameter
Note: The extrapolation is not performed unless either or both the EXFIRST and EXSECOND
keywords are specified.
Polyrate 189
Print:
Keyword Type Default Description
Others:
POTINF variable 0 print n pieces of PES information
PRPATH list not used print reaction-path information to units fu25-fu27
PRINTSTEP switch off print geom. at each save point
PRDISTMX variable 20 print interatomic distance matrices
PRSAVERP variable 9999 print geometry, V, and V ́at each save point
PRSAVEMODE variable 9999 print normal mode information at each save point
SDEBG1
variable
not used
s value for starting debug printing of generalized normal mode vibrational analysis along the MEP
SDEBG2
variable
not used
s value for ending debug printing of generalized normal mode vibrational analysis along the MEP
SPRNT variable 0 extra reaction-path Hamiltonian information printed at large s
SSPECPR switch off print information at special s values
Polyrate 190
Nonequilibrium Solvation:
Keyword Type Default Description
BATH list not used nonequilibrium solvation
BATHTEMP variable 298.0 temperature of the solvent in K
CUPLCNST list not used coupling constants in mass-scaled
atomic units (A)
DIFFUSION list not used diffusion coefficients in 10-5 cm2s-1
FRICTION variable 0 solvation time in fs
Torsional Anharmonicity
Keyword Type Default Description
SSTOR list not used MS-T torsional anharmonicity
along the reaction path by carrying
out a single-structure (SS)
calculation as described in Section
10.O.
MTOR variable no default local periodicities of torsions
Polyrate 191
Glossary of PATH keywords
BATH
BATH is a list keyword specifying the parameters used for a nonequilibrium solvation
calculation. For detailed description, see Ref. 53 in Sect. 21. There are 4 options:
Keyword Description
BATHTEMP temperature of the solvent in K
CUPLCNST atomic coupling constants of the solvent coordinate to the solute
in mass-scaled atomic units
DIFFUSION effective atomic diffusion constants in 10-5 cm2s-1
FRICTION solvent friction time in fs (Note: the friction time is also called
the solvation time)
Example: BATH
FRICTION 10.0 # in fs
DIFFUSION # in 10-5 cm^2s^-1
1 8.08
2 12.62
3 1.72
4 3.04
5 33.08
6 192.27
7 50.52
END
BATHTEMP 298.0
END
CARTRP (NOCARTRP)
The keyword CARTRP is used to declare explicitly that the reactant and product normal
mode analysis is carried out in Cartesian coordinates. The purpose of adding this
keyword is to allow the use of curvilinear coordinate normal mode analysis. In versions
of Polyrate earlier the 8.6, the normal mode analysis for reactants and products was
always carried out in Cartesian coordinates even though the normal mode analysis for
transition states can be carried out in curvilinear internal coordinates. The default is
CARTRP.
Note: CARTRP should not be used when scaling factors for principal force constants in
curvilinear internal coordinates (FCSCALE) are used.
Polyrate 192
COORD
COORD is a variable keyword specifying the type of coordinate system for calculating the
bound-state vibrational frequencies and normal mode eigenvectors along the MEP. It is
very important to use curvilinear coordinates rather than Cartesian coordinates for
generalized normal mode analysis along MEP in VTST calculations; Cartesian coordinate
will very likely yield imaginary frequencies along the reaction coordinate, which will
cause unphysical VTST results. See Sections 6.G.1 and 10.M. The default is cart
(Cartesian coordinates). The valid options are:
Option Definition curv1 use curvilinear internal coordinates for generalized normal
mode analyses using method of Ref. 41 of Sect. 21
curv2 use curvilinear internal coordinates for generalized normal
mode analyses using method of Ref. 43 of Sect. 21
curv3 use redundant internal coordinates for generalized normal
mode analyses using method of Ref. 46 of Sect. 21 cart use rectilinear, i.e., Cartesian coordinates for generalized
normal mode analyses
Note that if the curv1, curv2, or curv3 option is used, the INTDEF keyword
discussed below is required.
Example: COORD curv2
CURV
CURV is a variable keyword used to specify the method for computing the reaction path
curvature components. See Sections 6.H and 10.F for more information about this issue. The default is dgrad. The valid options are:
Option Definition
dgrad use a quadratic fit to obtain the derivative of the gradient with
respect to the reaction coordinate
oneside use one-sided differences for the derivative of the gradient
with respect to the reaction coordinate dhess use Hessian, generalized-normal mode eigenvectors, and
gradient to calculate the reaction path curvature
Example: CURV dgrad
Polyrate 193
DLX3
DLX3 is a variable keyword for specifying the step size used for numerical differentiation
in unscaled atomic Cartesians to obtain the 3rd derivatives of V from the Hessian at the
saddle point. These derivatives are required when the cubic starting algorithm is
employed (see FIRSTSTEP). The default unit is angstroms and it can also be in bohr by
specifying the keyword INPUNIT AU. The default is 1 10-4 ao.
Example: DLX3 0.00005
ES1OPT
ES1OPT is a list keyword for using the Euler with stabilization integrator. The user must
give the step size for the finite-difference derivative (DELTA2 keyword) and the tolerance
parameter for the magnitude (in a.u.) of the difference vector between successive
normalized gradients (DIFFD keyword). See Section 10.D. The default unit of step size
DELTA2 is angstroms and it can also be in bohr by specifying the keyword INPUNIT AU.
The defaults are DELTA2 = 5 10-5 ao and DIFFD = 1 10-8.
Example: ES1OPT
DELTA2 0.00001
DIFFD 0.000001
END
EXFIRST
EXFIRST is a list keyword for specifying the extrapolation beyond the limits (SLM and SLP)
of the Hessian grid for the first direction from the saddle point when using the hooks.
(See Section 7.B for a discussion of which direction is first.) The EXFIRST and EXSECOND
keywords cannot be used with units fu30, fu31, or fu40. The extrapolation procedure is
different for reactions with and without a saddle point. The particular extrapolation
procedure to be used is chosen based on the SADDLE(NOSADDLE) keyword in the PATH
section.
For reactions without a saddle point (NOSADDLE specified in the PATH section) the
extrapolation procedure is described in Section 10.A; it is designed to extrapolate VaG(s)
and meff ( )s toward bimolecular reactants or products and should not be used to
extrapolate toward unimolecular reactants or products. If EXFIRST is omitted, no
extrapolation is performed in the first direction, that is, by default no extrapolation is
performed. If no extrapolation is performed, VMEP is set equal to the reactant or product
value beyond the limits, and eff is set to .
Polyrate 194
For reactions with a saddle point (SADDLE is specified in the PATH section; or SADDLE is
accepted as the default) the extrapolation procedure is based on the mapped interpolation
algorithm, which is described in Sections 6.N.3 and 10.J and in Ref. 48 of Sect. 21. The
mapped interpolation algorithm is used to extrapolate VMEP, | I |, , and BmF. If EXFIRST
is omitted, no extrapolation is performed in the first direction, that is by default no
extrapolation is performed.
The EXALPHA keyword is only used for reactions without a saddle point.
If the EXFIRST keyword is not specified, then no extrapolation is performed. If the
EXFIRST keyword is specified with an empty list then the extrapolation is performed with
the default values listed below. The keywords in this list and their respective default
values are explained below.
Keyword Description Default
EXREACT extrapolation is towards reactants off
EXPROD extrapolation is towards products on
EXNSTEP number of steps to be taken in extrapolation region 0 EXSTEP mass-scaled step size in the extrapolation region 0.03 ao
for computing the adiabatic potential and other
quantities needed for the tunneling calculations. The
default unit is angstroms and it can also be in bohr by
specifying the keyword INPUNIT AU.
EXALPHA exponential range parameter in reciprocal angstroms (only
used with NOSADDLE). It can also be in reciprocal bohrs by
the keyword INPUNIT AU. 1.0 ao-1
Example: EXFIRST
EXPROD
EXNSTEP 50
EXSTEP 0.1
EXALPHA 0.5
END
Example (empty list, defaults only): EXFIRST
END
Polyrate 195
EXSECOND
EXSECOND is a list keyword that is very similar to EXFIRST but is used for specifying the
extrapolation beyond the limits (SLM and SLP) of the Hessian grid for the second direction
from the saddle point when using the hooks. (See Section 7.B for a discussion of which
direction is first.) The EXFIRST and EXSECOND keyword can not be used with units fu30,
fu31, or fu40. See also the discussion of EXFIRST. The EXALPHA keyword is only used
when NOSADDLE is specified in the PATH section. If the EXSECOND keyword is not
specified then no extrapolation is performed. If the EXSECOND keyword is specified with
an empty list then the extrapolation is performed with the default values listed below.
The valid keyword options are defined below.
Option Description Default
EXREACT extrapolation is towards reactants on
EXPROD extrapolation is towards products off
EXNSTEP number of steps to be taken in extrapolation region 0
EXSTEP mass-scaled step size in the extrapolation region 0.03 ao
for computing the adiabatic potential and other quantities
needed for the tunneling calculations The default unit is
angstroms and it can also be in bohr by specifying the keyword
INPUNIT AU.
EXAPLHA exponential range parameter in reciprocal angstroms. It can
also be in reciprocal bohrs by the keyword INPUNIT AU. 1.0 ao-1
Example: EXSECOND
EXREACT
EXNSTEP 50
EXSTEP 0.1
EXALPHA 0.5
END
Example (empty list, defaults only): EXSECOND
END
FCSCALE
FCSCALE is a list keyword used to specify scaling factors for principal force constants of
the selected curvilinear internal coordinates defined in the INTDEF keyword. This
keyword should be used only when internal coordinates defined by COORD curv2 or
COORD curv3 options are used, and the switch keyword FREQ is on. To specify the
selected curvilinear internal coordinates involving force constant scaling, the
connectivities of atoms are required to be defined using the INTDEF keyword as well as
the FCSCALE keyword is used. Each item in the list is in the form of an integer sequence
Polyrate 196
number followed by a floating-point scaling factor. The sequence number denotes the
ordinal number of the specific coordinate in the list of all the curvilinear internal
coordinates defined under the INTDEF keyword. (Note: This is not the ordinal number in
internal storage after the code internally re-orders the coordinates.) The corresponding
diagonal element in the force constant matrix will be scaled by the scaling factor. All
scaling factors are set to 1.0000 as the default. In the following example, the sequence
number 8 in FCSCALE represents the stretch between atom 1 and atom 2; thus the diagonal
element in the force constant matrix involving that stretch will be scaled by a scaling
factor of 0.9734.
Example:
INTDEF
1=2=3
2-3-4 2-3-5 2-3-6 4-3-5 4-3-6 5-3-6 1-2 2-3 3-4 3-5 3-6
4-3-5-6
END
FCSCALE
8 0.9734
END
When FCSCALE is used, NOCARTRP should be declared explicitly because the reactant and
product normal mode analysis should be carried out in curvilinear coordinates.
The actual effect of the force constant scaling is controlled by the keyword SCLPT, in
which either the scaling of the potential or the scaling of frequencies is specified. The
default is scaling the frequencies only (NOSCLPT).
Note: Another different way to scale frequencies is with FREQSCALE, in which all
frequencies are scaled by the same scaling factors.
FIRSTSTEP
FIRSTSTEP is a variable keyword specifying the method for taking the first step off the saddle point or starting geometry. The default is nmode. The valid arguments are:
Option Definition
nmode take the first step along the imaginary-frequency normal
mode
cubic use the cubic starting algorithm (see STEP 3)
gradi take the first step along the negative of the gradient direction
[ use this only if NOSADDLE is selected; see Section 6.G ]
Example: FIRSTSTEP cubic
Polyrate 197
FREQSCALE
FREQSCALE is a variable keyword for specifying the factor by which to scale the harmonic
vibrational frequencies for partition function calculations. If FREQSCALE is used, the
scaling will be applied to all stationary point frequencies and generalized normal mode
frequencies for generalized transition states along the reaction path. Furthermore, the
vibrationally adiabatic potential energy curve VaG will be calculated by adding the scaled
ZPE to VMEP and all tunneling calculations will be based on this new VaG. The default is
not to scale the frequencies. For kinetics, the scale factor that one should choose is the
one for reproducing the correct ZPE, i.e., the ZPE scale factor, which is available on the
website: https://comp.chem.umn.edu/freqscale/version3b2.htm.
Please notice that, if the vibrational frequencies are directly read in from the .dat
input file, the FREQSCALE will not be applied on these user-input vibrational
frequencies; and therefore, usually, the user-input frequencies in .dat file should have
already been scaled by the user with the same frequency scale factor for the reaction path.
This feature thus also provides the user with an opportunity to use different scale factors
for stationary points and for the saddle point and the non-stationary points on the reaction
path.
Example:
FREQSCALE 0.91
FREQINCR
FREQINCR is a variable keyword for specifying the value to which the frequencies that are
lower than this value to increase (unit is cm-1)
Example:
FREQINCR 200
HESS (NOHESS)
HESS is a switch keyword that determines if the Hessian should be computed along the
MEP. This switch is defaulted to on and in most cases one would want to compute the
Hessian. Most likely this switch will only be used for a special case when the Hessian is
not desired, and thus NOHESS will be used. The default is HESS.
Polyrate 198
IDIRECT
IDIRECT is a variable keyword used to specify the direction of the initial step from the
starting point. The allowed arguments for this variable are ±1: +1 if the initial direction
is the direction toward products and -1 if it is towards reactants. See Section 7.B. The
default is 1.
Example: IDIRECT 1
INH
INH is a variable keyword used to specify the ratio of the number of gradients to the
number of Hessians calculated along the MEP. INH must be an integer value. The
default is 9.
Example: INH 4
INI
INI is a variable keyword used to specify the interval of the gradient interpolation steps in
the IVTST-M calculation. INI must be an integer value less than or equal to INH. The
default is 1.
Example: INI 2
INTDEF
INTDEF is a list keyword used to specify the curvilinear internal coordinates used for the
vibrational frequencies and calculations of generalized normal modes. (It is very
important to use curvilinear coordinates rather than Cartesian coordinates for VTST
calculations; Cartesian coordinate will very likely yield imaginary frequencies along the
reaction coordinate, which will cause unphysical VTST results.) The allowed types are
• stretches (i-j),
• bends (i-j-k),
• dihedrals (i-j-k-l), and
• doubly degenerate linear bends (i=j=k)
where i, j, k, and l are the atom-number-labels defined in the GENERAL section.
Note: when the bond angle is close to 180 degrees (i.e., greater than about 175 degrees),
using the doubly degenerate linear bending mode approximation will prevent dividing by
zero or a number close to zero during computations.
Polyrate 199
Example: INTDEF
1-2 1-3 3-4 2-1-3 1-3-4 2-1-3-4
END
Note: The pound sign (#) cannot be used as a comment card within the INTDEF keyword
list.
INTMU
INTMU is a variable keyword that indicates the number of points on each side of the
saddle point used for the interpolation of the effective reduced mass at the saddle point.
See Section 6.H. The default value is 1. The valid options are:
Option Definition
1 1 point on either side of the saddle point; thus interpolation is
based on 2 points
3 3 points on either side of the saddle point; thus interpolation is
based on 6 points
Example:
INTMU 1
ISWP
ISWP is a variable keyword for specifying the index of the product frequency that will be
scaled by a factor of (VSCALE)1/2. This keyword is only needed if the VSCALE keyword
is specified and there is only one product species.
Example: ISWP 9
ISWR
ISWR is a variable keyword for specifying the index of the reactant frequency that will be
scaled by a factor of (VSCALE)1/2. This keyword is only needed if the VSCALE keyword
is specified and there is only one reactant species.
Example: ISWR 9
Polyrate 200
IVTSTMOPT
IVTSTMOPT is a list keyword for specifying the IVTST-M options for the curvature
components and unimolecular reactions.
The mapping procedure for the curvature components is slightly different from the
mapping for the rest of the parameters. The exponent in equation 19 of Ref. 48 in Sect. 21
has been optimized in order to make the changes of the interpolated curvature
components along the reaction path as close as possible to the changes observed in
converged calculations. Therefore, the user is strongly advised against changing this
parameter without a good reason. If one does have a good reason, though, the exponent
can be set by means of the LBEXP variable option. This keyword can only take positive
odd integer values.
There are two methods for performing IVTST-M calculations for the unimolecular side
(or sides) of reactions with one reactant or/and one product, or wells in one of the
channels: (i) to carry out a spline-under-tension fit (as a function of z) based only on the
input data, or (ii) to carry out a spline-under-tension fit based on ten extra energy points.
The ten extra points are calculated by means of a cubic polynomial fitted to the
unimolecular reactant, unimolecular product, or well, a point calculated from the lowest
real frequency at that minimum, and the two points on the reaction path with the largest
|s| values on the unimolecular side. In the second option generating the extra point from
the frequency requires the choice of a small step-size, whose value is recommended to be
the same as the gradient step-size used in the calculation. The polys option specifies the
treatment to be given to the unimolecular side (or sides), and, the sincw option specifies
the value of the step-size. The default is to use a cubic polynomial for estimating 10 extra
energies, with a step-size along the lowest frequency mode of 0.01 a0 in s, which is mass
scaled.
Option Definition
lbexp value of the exponent for interpolating the curvature components.
The default is 3. polys use a cubic polynomial for estimating 10 energy points before
spline-fitting VMEP(s).
polyz use a cubic polynomial for estimating 10 energy points before
spline-fitting VMEP(z) (default).
nopolys do not include 10 extra points, and base the spline fit on input
data only plus one extra computed as described in Section 10.J.
sincw variable keyword to indicate the step-size along the lowest-
frequency mode to fit the cubic polynomial. The default unit is
mass-scaled angstroms and it can also be in mass-scaled bohr by specifying the keyword INPUNIT AU. The default value is 0.01 a0.
this value is used only if polys or polyz is selected.
Polyrate 201
fixmuef keyword used to apply a global interpolation to estimate the
effective reduced mass eff of the SCT algorithm at the saddle
point when the IVTST-M algorithm is used with hooks. The
default option is to use local Lagrangian interpolation for the
effective reduced mass at the saddle point with either one point
or three points (see INTMU keyword option) one each side of the
saddle point. The global interpolation can be used to obtain a
smoother value of eff at the saddle point; it should be used if
and only if the points close to the saddle point suffer from
numerical instability.
tension keyword used to specifically give a tension factor in interpolation
using spline under tension. If this keyword not used, the program
will automatically determine the tension factors. The value for
this keyword must be between 0 an 85. We recommend to use
this keyword only in case very large tension factor is needed.
Example: IVTSTMOPT
lbexp 5
polys
sincw 0.005
END
Polyrate 202
IVTST0FREQ
IVTST0FREQ is a list keyword that modifies the frequency of a particular mode along the reaction path. A section for each mode begins with the list option keyword MODE which contains lines with the following keyword options:
Option Definition
index index of the vibrational mode to be interpolated (this is
determined from the frequencies of the saddle point arranged in
decreasing order).
reactant x used to indicate the frequency (in cm-1) at the reactant side (s <
0) for the interpolation with value x. When the reactant is
unimolecular or a reactant well present, the s value has to be
provided with option SR. If a reactant well exists for a
bimolecular reaction, the interpolation uses the frequency at the
well instead of the reactants.
start x used to indicate the frequency at s = 0 for the interpolation.
product x used to indicate the frequency at the product side (s > 0) for the
interpolation with value x. When the product is unimolecular or
a product well present, the s value has to be provided with option
SP. If product well exists for a bimolecular reaction, the
interpolation uses the frequency at the well in stead of the
products. sr x used to indicate the s value at the limit of reactant side (s < 0).
The default unit is angstroms and it can also be in bohr by
specifying the keyword INPUNIT AU. The default value is −1.0
bohr.
sp x used to indicate the s value at the limit of product side (s < 0).
The default unit is angstroms and it can also be in bohr by
specifying the keyword INPUNIT AU. The default value is +1.0
bohr.
The IVTST0FREQ algorithm is similar to the frequency interpolation algorithm of the VTST-IC method. See Section 10.M for a detailed description. Notice that IVTST0FREQ can be used to interpolate a given mode, say i, (where modes are numbered in order of decreasing frequency) from the saddle point to reactants and products. It cannot interpolate between mode i at the saddle point and mode i + 1 at reactants (which might sometimes be useful for unimolecular reactions). It cannot interpolate between mode i at the saddle point and mode i at an intermediate location between the saddle point and reactants. Note that IVTST0FREQ is currently incompatible with using fu31.
Example: For a bimolecular/bimolecular case
IVTST0FREQ
Polyrate 203
MODE
index 11 reactant 0
start 300 product 0 END
END For a unimolecular/bimolecular case
IVTST0FREQ
MODE index 11
reactant 50 start 200 product 0
sr -2.0 END END
NEXTPT (NONEXTPT)
NEXTPT is a switch keyword that only works if POTENTIAL = unit30 or unit 40.
When turned on it will cause Polyrate to compute only the next point on the MEP by
taking a single step from the last point in the electronic structure input file, and then stop.
The method used for the step will be ESD (default), or Page-McIver (if PAGEM is
specified). The step size used in this procedure is specified using the SSTEP keyword.
The direction in which one is following the path (towards reactants or products) is
specified using the IDIRECT keyword in conjunction with NEXTPT (IDIRECT = 1 to calculate
the next point to the right; IDIRECT = -1 to calculate the next point to the left). For
example, using the ESD method, turning on NEXTPT causes the following calculation to
be performed
xnext-point = xcurrent – s gcurrent
snext-point = scurrent + (IDIRECT) s
where xcurrent is the mass-scaled geometry corresponding to the last point input on fu30
or fu40, and ˆ g current
is a unit vector in the direction of the mass-scaled gradient at that
point. Thus, to go left, the last point read in should have negative s, and to go right, it
should have positive s.
This option is useful when using Polyrate as a driver to determine geometries for ab
initio calculations. The only print option in unit fu30 compatible with the use of NEXTPT
is LOPT(1) = 0. The default is NONEXTPT.
Polyrate 204
NSTEPS
NSTEPS is a variable keyword for specifying the maximum number of steps (after the first
step) along the negative of the gradient of V to be taken in each direction from the saddle
point or starting full-system geometry. The minimum number of steps is the number
required to reach the limits specified by SRANGE. The default is 99999.
Example: NSTEPS 5000
POTINF
POTINF is a variable keyword that specifies how many pieces of data from the potential
energy subroutine are written along the MEP to FORTRAN unit fu6. The default is 0.
See Subsection 8.C.1 for details.
Example:
POTINF 4
PRDISTMX
PRDISTMX is a variable keyword that indicates the interval along the Hessian grid for the
printing of interatomic distance matrices. The i-j element of the interatomic distance
matrix is the distance (in mass-scaled bohr) between atoms i and j. The default is set to
print the interatomic distance matrix at every 20th point along the Hessian grid.
Example: PRDISTMX 20
PRINTSTEP (NOPRINTSTEP)
PRINTSTEP is a switch keyword that specifies that the geometry at each step along the
MEP be printed in fu6 output file. The default is NOPRINTSTEP. See the SPRNT keyword
below.
PRPATH
PRPATH is a list keyword used to set the options for printing reaction-path information to
units fu25-fu27. This keyword is especially useful for analyzing reaction-path data. The
unit fu25 and fu26 output can easily be imported to a spreadsheet, and unit fu27 output is
designed to be read into the XMOL program to visualize the geometry changes along the
reaction path. (The XMOL program is a X-windows-based molecule viewer and format
converter developed by Wasikowski and Klemm at the Minnesota Supercomputing
Center, Inc.) When this keyword is specified, the program will automatically write the
energetic information (VMEP and VaG) to unit fu25. The valid options are defined below.
Polyrate 205
Option Description Default coord ai up to 4 atoms, from the full system, can be specified off
for which the bond distances(2, 3, or 4 atoms specified),
the bond angles(3 or 4 atoms specified), and the dihedral
angle(4 atoms specified) are calculated and written to unit
fu28.
interval n write the reaction-path information every n Hessian grid 1
points.
freq mi GTS frequency mode numbers to be printed to unit fu26; not used
a total of up to ten modes can be specified and printed.
xmol write XMOL XYZ input file to unit fu27. off
Example: PRPATH
COORD 1 2 3 6
INTERVAL 5
FREQ 1 2 3
XMOL
END
PRSAVEMODE
PRSAVEMODE is a variable keyword that specifies that (in addition to the items listed for
PRSAVERP) the normal mode eigenvectors, energies, curvatures, and frequencies be
printed at a given multiple of the save point. The default is 9999.
PRSAVERP
PRSAVERP is a variable keyword that specifies that the geometry, potential (V), curvatures,
and gradient (V )́ at a given multiple of the save point along the MEP be printed. The
default is 9999.
REORDER (NOREORDER)
REORDER is a switch keyword that specifies that the frequencies be ordered according to
overlap calculations along the MEP. The default is NOREORDER, which means the
frequencies are in canonical order. See Sections 6.E, 6.F, and 6.G for further discussion.
Polyrate 206
RODS (NORODS)
RODS is a switch keyword which specifies that the RODS algorithm is to be used to re-
orient the generalized transition state theory dividing surface. The RODS algorithm can
be used with any of the integrators, ESD, ES1, or PAGEM. See Sect. 10.D. The default
is NORODS, which turns RODS off. When RODS is off, the generalized-transition-state-
theory dividing surface is normal to the gradient.
RPM
RPM is a variable keyword that indicates which integrator is to be used for following the
reaction path. The default is esd. The valid options are defined below.
Option Description esd use the Euler steepest-descents integrator to follow the reaction
path; this is the name we now use for the Euler algorithm, which
is often called the Euler single-step algorithm in textbooks
es1 use the Euler-with-stabilization integrator to follow the reaction
path
pagem use the Page-McIver integrator to follow the reaction path
vrpe use the VRP(ESD) algorithm to follow the reaction path
Example:
RPM pagem
SADDLE (NOSADDLE)
SADDLE is a switch keyword to indicate whether the reaction has a saddle point or not.
See Sect. 6.G. The default value is SADDLE.
SCALEMASS
SCALEMASS is a variable keyword for the reduced mass µ in amu used in defining the
mass-scaled coordinates. This reduced mass is called the scaling mass. See Refs. 1 and 5
of Sect. 21 for an explanation of the scaling mass. Notice that no physical observable
depends on µ, but a single value must be used consistently in the whole calculation. Note
also that certain nonobservable intermediate quantities, most notably the numerical value
of s at any point along the MEP, do depend on µ. The default is 1.0 amu which means
that the mass-scaled coordinates in bohrs have the same numerical values as mass-
weighted coordinates in amu1/2 bohrs. (These are the mass-weighted coordinates made
popular by Wilson, Decius, and Cross in Ref. [36] of Sect. 22.) The variable µ is
discussed in Section 6.A of this manual.
Example: SCALEMASS 0.195
Polyrate 207
SCALERP
SCALERP is a switch keyword for scaling previously calculated frequencies that appear in
the VIB section of input. This keyword is off by default. Frequencies that have already
been calculated with the FREQSCALE option are scaled, and therefore this option would
not be required. Frequencies that have been calculated without scaling, and then used
with the FREQSCALE option would require this keyword in order for the program to scale
them correctly.
SCLPT (NOSCLPT)
SCLPT is a switch keyword to specify the behavior of the force constant scaling option.
(Note: Details of the force constant scaling option can be found in the description of the
keyword FCSCALE).
If the keyword SCLPT is turned on along with the keyword FCSCALE, the potential surface
is actually scaled. The scaled force constant matrix will be used to obtain both the
frequencies and the normal mode eigenvectors in the normal mode analysis. Thus the
MEP is altered when FCSCALE is used with those force-constant involved reaction-path
following algorithms, such as VRP(ESD), Page-McIver, etc. Also, the first step on the
reaction path will be changed as well if the normal mode eigenvector with the imaginary
frequency is used to determine the direction of the first step.
However, if this switch is turned off using NOSCLPT, the force constant scaling is actually
just a way to change some of the frequencies. After frequencies are obtained from the
scaled force constant matrix, the un-scaled force constants are recovered. The normal
mode eigenvectors all come from the un-scaled force constants. Users should be aware
that the MEP is not altered using this strategy. The only quantity changed is the
frequencies. Those scaled frequencies will be used in the calculations of ZPE, vibrational
partition functions, and tunneling probabilities.
SDEBG1
SDEBG2
SDEBG1 and SDEBG2 are variable keywords used to specify the s limits of the interval on
the MEP at which to have debug information of the vibrational frequencies and
generalized normal-mode calculations output to unit fu6. The default unit is angstroms
and it can also be in bohr by specifying the keyword INPUNIT AU. (Note: the value of
SDEBG1 has to be smaller than SDEBG2).
Example: SDEBG1 0.499
SDEBG2 0.501
Polyrate 208
SFIRST
SFIRST is a list keyword that allows a special step size for the first n steps. The user must
give the number of initial steps to be taken in each direction from the initial geometry,
including the initial step (NFSTEP) and the step size for each of these steps (FSIZE). The
default unit of FSIZE is angstroms and it can also be in bohr by specifying the keyword
INPUNIT AU. The defaults are NFSTEP = 0 and FSIZE = 1 10-5 ao.
Example: SFIRST
NFSTEP 10
FSIZE 0.0001
END
SIGN
SIGN is a variable keyword used to ensure the conventional definition of the sign of s,
s < 0 for the reactant side and s > 0 for the product side, is followed. The allowed
arguments for this variable are reactant and product: product if the unbound
eigenvector at the saddle point points toward the product side and reactant if the
eigenvector points toward the reactant side. The SIGN keyword is discussed further in
Section 7.B. The default is reactant.
Example: SIGN product
Polyrate 209
SPECSTOP
SPECSTOP is a list keyword that may be used to specify the range over which the MEP is
to be computed. This keyword can function in conjunction with the SRANGE keyword
that is presented below. The SPECSTOP keyword may be used to limit the range over
which the MEP is calculated to a smaller range than that specified by the SRANGE
keyword. The MEP calculation will be stopped when the value of the potential energy
(VMEP) or the value of the vibrationally adiabatic ground-state potential energy (VaG)
becomes smaller than a critical value. This critical value is defined based on the values
of potential energy or zero-point-inclusive potential energy at the saddle point and
reactants or products. For example, if the VaG curve is chosen, the MEP will be
determined until the VaG(s) becomes smaller then the value calculated as: [(1-x) VaG(s=0)
+ x V+ZPE(R or P)] where V+ZPE(R or P) is the higher of the zero-point-inclusive
potential energy for the reactants and products, and x is equal to X/100 (X is the argument
of PERCENTDOWN subkeyword). Note that V+ZPE(R or P) is equivalent to VaG(R or P)
for a bimolecular reaction but not for an unimolecular reaction for which VaG(R or P)
does not include the zero-point-energy contribution of the reaction coordinate motion.
Similarly, if the VMEP curve is chosen, the MEP will be calculated until the VMEP(s)
becomes smaller then the value calculated as: [(1-x) VMEP(s=0) + x VMEP(R or P)] where
VMEP(R or P) is the higher of the zero-point-exclusive potential energy for the reactants
and products, and x is again equal to X/100 (X is the argument of PERCENTDOWN
subkeyword). Finally, the MEP limits can be chosen either on the fine grid (also called
gradient grid) or the save grid. In the current version of the code, this keyword cannot be
used if the calculation requires the use of a restart file (fu1, fu2, or fu3) or the use of an
electronic structure input file (fu29, fu30, fu31, or fu40). The valid keyword options are
defined below.
Option Description Default*
CURVE the curve on which comparison is made vag
(the options are vmep and vag)
POINT the grid on which the end point is chosen savegrid
(the options are savegrid and finegrid)
PERCENTDOWN percent down from the saddle point 50.
Example: SPECSTOP
CURVE vmep
POINT finegrid
PERCENTDOWN 63.4
END
Example (empty list, defaults only): SPECSTOP
END
Polyrate 210
* These are the defaults if SPECSTOP is specified. If it is not specified, then PERCENTDOWN is
effectively infinity, i.e., only SRANGE is used to stop the reaction path calculation.
SPRNT
SPRNT is a variable keyword that, if PRINTSTEP is on, requires that |s| > SPRNT for any
reaction-path information to be printed. Default is 0. The default unit is angstroms and it
can also be in bohr by specifying the keyword INPUNIT AU.
Example: SPRNT 0.1
SRANGE
SRANGE is a list keyword needed to specify the limits on the reaction coordinate, s for
which the MEP is to be computed. These limits, SLM and SLP, are the ranges over which
the MEP is computed, i.e., SLM s SLP. The default unit is angstroms and it can also be in bohr by specifying the keyword INPUNIT AU. The default values are SLM = –1.0 ao and
SLP = +1.0 ao.
Example: SRANGE
SLP 1.50
SLM -1.75
END
SSPECIAL
SSPECIAL is a list keyword used to give all the special s values at which normal mode
analyses are to be performed. These values of s will be included in the Hessian grid. The
default unit is angstroms and it can also be in bohr by specifying the keyword INPUNIT
AU. The default is to not include any special s values. See keyword SSPECPR below.
Example: SSPECIAL
0.14
0.34
-0.76
END
Polyrate 211
SSPECPR
SSPECPR is a switch keyword that works in conjunction with SSPECIAL. It turns on the
printing of generalized normal mode vibrational energies, frequencies, and eigenvectors
for the special s values regardless of whatever other print keywords are specified. The
default is off.
SSTOR
SSTOR is a list keyword that specifies the parameters used for the torsional-potential
anharmonicity calculations along reaction path by the SS-T method. Note that when only
a single structure among all conformational structures is considered, the MS-T method is
reduced to the SS-T method as described in Section 10.O. The SSTOR keyword also turns
on the SS-T calculations along reaction path. The valid keyword options are defined
below.
Option Description Default*
MTOR local periodicities of torsions, i.e. M j,t values no default
Example: SSTOR
MTOR 3 3 3 3
END
SSTEP
SSTEP is a variable keyword that specifies the step size along the mass-scaled MEP for
following the gradient of V, except that the first n steps can be different (see SFIRST). The
default unit is angstroms and it can also be in bohr by specifying the keyword INPUNIT
AU. The default is 5 10-4 ao.
Example: SSTEP 0.0001
Note that SSTEP is ignored if POTENTIAL = unit30, unit31, or unit40 is specified in the
GENERAL Section. See Section 9.C.
SYMMETRY (NOSYMMETRY)
SYMMETRY is a switch keyword that specifies that the reaction path is symmetric. When
this is turned on only one direction of the MEP from the saddle point is calculated, and
the MEP information from the other direction is obtained by reflection. Default is
NOSYMMETRY.
Polyrate 212
VSCALE
VSCALE is a variable keyword for specifying the factor by which to scale the potential
energy along the MEP. If VSCALE is 0 or 1, no scaling is done. The default is 1.
Example: VSCALE 1
Polyrate 213
12.A.8. TUNNEL section
The TUNNEL section contains the keywords that control the tunneling calculations. This
section is not needed if tunneling calculations are not desired. If this section is not
included then all defaults are ignored, and the default SCT, ZCT, and Wigner calculations
are not performed. For simplicity the keywords have been broken into two categories:
basic and large-curvature. This is only for clarity in the manual. The keywords in any of
these categories can be used in any order. Also for simplicity the keywords in each
category have been labeled as either common or other. The keywords labeled common
are those that might be expected to be found reasonably frequently in input files for
typical Polyrate runs. This labeling is only intended as an aid to the novice user. Again
an alphabetical glossary of all the keywords follows the two summary tables.
Polyrate 214
Basic:
Polyrate 215
Keyword Type Default Description
Common:
SCT switch on small-curvature tunneling
ZCT switch on zero-curvature tunneling
Others:
EMIN variable 0 cutoff E for computing percent
tunneling
QRST list not used quantized-reactant-state tunneling
HARMONIC switch on harmonic approximation
HARMWKB switch off harmonic-WKB approximation
SYMWKB switch off WKB and symmetric VaG
MODE variable required number of the selected vibrational
reaction-path mode
SRW variable required s value of the reactant
STATES variable all number of states included in
calculation
QUAD list no changes change quadrature parameters
NSEGBOLTZ variable 1 segments for Boltzmann integral
NSEGTHETA variable 1 segments for theta integral
NQE variable 40 quadrature points for Boltzmann
integral
NQTH variable 40 quadrature points for theta integral
SCTOPT list spline small-curvature tunneling options
LAGRANGE variable 4 Lagrange interpolation for eff
SPLINE switch on spline fit for interpolating eff
WIGNER switch on Wigner tunneling
Polyrate 216
Large-curvature tunneling:
Keyword Type Default Description
Common:
ALLEXCIT switch on tunneling into all excited states
EXCITED variable 0.0 tunneling into nth excited state
LCT switch off large-curvature tunneling
LCTDETAIL list not used print extra details in LCT
calculations
Others
LCTOPT list not used large-curvature tunneling options
ILCT switch off interpolated LCG calculation
INTERPOLATE variable 4 order of interpolation (see glossary)
LCGMETHOD variable 4 method for LCT calculations
LCTRST switch off restart a previous LCT calculation
LCTSTR switch on store information from a LCT calculation for a possible restart
NGAMP variable 120 quadrature points for tunneling
amplitude
NGTHETA variable 120 quad. pts. for theta integral
NILCGPT variable 9 number of interpolated points at each tunneling energy
PRFREQ switch off print information (see glossary)
PRPROB switch off print uniform probabilities
RTPJAC switch off print information in pseudo-Jacobian coordinates
VADAVG switch off average the overlapping of two adiabatic potentials
VEFSRCH variable 999 search for possible nonadiabatic LCG4 regions
Polyrate 217
Glossary of TUNNEL keywords
ALLEXCIT (NOALLEXCIT)
ALLEXCIT is a switch keyword that specifies that the large-curvature tunneling
calculations (see LCT) are to be performed with tunneling into all accessible excited states
in the LCT exit arrangement. Default is on. The opposite switch, NOALLEXCIT, specifies
that tunneling calculations be performed with tunneling into only the ground state.
Note that the maximum number of excited states is set by the MAXPS parameter in the
aamod.f90 file (see Subsection 5.A.2).
EMIN
EMIN is a variable keyword whose argument specifies the energy (in kcal/mol) that is the
cutoff point in computing the percent tunneling that comes from below Emin. The default
is 0.0.
Example: EMIN 48.35
EXCITED
EXCITED is a variable keyword whose argument is the state n. The LCT tunneling
calculation is performed with tunneling into up to the state with quantum number n,
where n = 0,1,.... Default is 0. The example below is for the case where tunneling will
be performed for the first excited state in the LCT exit arrangement (if accessible) as well
as for the ground state. Note that this keyword shouldn’t be used together with the
ALLEXCIT or NOEXCIT keyword.
Example: EXCITED 1
LCT3 or LCT4
One of these two keywords is compulsory if large curvature calculations are required.
The default is off. If LCT3 (the old LCT) or LCT4 (see Section 10.4. for details) are on,
then the COMP and OMT results (described in Section 6.I) are always calculated. Of
the two options (LCT3 and LCT4), LCT4 is recommended; LCT4, being the final
version, is usually just denoted LCT.
Polyrate 218
LCTDETAIL
LCTDETAIL is a list keyword that prints extra details of the LCT calculations to Fortran
unit fu41 to fu47 files. The valid subkeyword options are defined below. See Section 14.
Option Description
state n n is the quantum number of the vibrational state (0 is the
ground state) for which information is to be printed. interval m m is the number of intervals of the energy grid the user wants
to print out for this particular quantum state; LB and UB are
lb1 ub1 the indices of the lower and upper bounds of the energy
lb2 ub2 grid interval, respectively.
:: lbm ubm
Example: LCTDETAIL
STATE 0
INTERVAL 2
20 22
30 32
STATE 1
INTERVAL 1
30 31
END
LCTGRID
This is a list keyword that specifies the grid to carry out the ILCT1D or ILCT2D
calculations. The valid options are defined below
Option Description
state n n is the quantum number of the vibrational state (0 is the ground
state) for which information is to be printed.
Npoints are the single point energy calculations carried out at each
tunneling energy and fitted to a spline. Npoints must be specified
with ILCT1D. The default is Npoints equal to 9.
NumberE NumberX The 2D grid to perform the ILCT2D calculation can be specified
here. NumberE are the number of tunneling energies and
NumberX is the number of points within each tunneling energy.
LCTOPT
LCTOPT is a list keyword that is used to set options for the large-curvature tunneling
calculations. If this keyword is used, then it is assumed that the large-curvature tunneling
Polyrate 219
calculations are desired and LCT is automatically switched on. The valid options are
defined below.
Polyrate 220
Option Description Default ILCT1D This switch keyword is used to calculate LCT3 or
LCT4 transmission factors. At each tunneling
energy performs a 1D spline under tension fit of the
nonadiabatic region. The number of energies
calculated along a given tunneling path is specified
in LCTGRID.
off
ILCT2D This switch keyword can be used either to calculate
LCT3 or LCT4 transmission factors, although we
recommend its use to evaluate only the latter. This
is a 2D spline under tension fit based on a grid of
tunneling energies and points along the tunneling
path for each tunneling energy. The grid is
specified in LCTGRID.
off
interpolate order of interpolation used for the LCG3 theta
integrals, the excited state potential, the vibrational
period, and the sine of the angle between the MEP
and the tunneling path.
4
lcgmethod Select the method for LCT calculations. Two
values are possible: 3 and 4, for LCG3 and LCG4
methods respectively.
4
lctrst restart a previous large curvature calculation from
unit fu48. This is useful to calculate LCT4
transmission factors from a previous LCT3 run.
off
lctstr store information in unit fu49 for a possible restart. on ngamp number of points for Gauss-Legendre quadrature
and trapezoidal rule in computing the total tunneling amplitude along the incoming trajectory in the LCG3 and LCG4 methods.
120
ngtheta number of points for Gauss-Legendre quadrature in
computing the theta integral over the straight-line
tunneling path in the LCG3 and LCG4 methods
120
prfreq print information in fu22 file about the frequency of
the mode p(s), the classical energy VMEP(s), and the
vibrationally adiabatic potential energy as a
function of s and np(Va(np,s)), and all the
uniformized probabilities at each np.
off
prprob print all uniformized probabilities at each np to fu22 off rtpjac print the MEP and representative tunneling path
turning points in mass-scaled pseudo-Jacobian
coordinates to fu24
off
vadavg average the overlapping of two adiabatic potentials
instead of choosing the minimum of them.
off
vefsrch numb search for possible nonadiabatic LCG4 regions in
totally adiabatic LCG3 regions. The search starts
from that tunneling energy until numb
0
Polyrate 221
Example: LCTOPT
lctrst
ngamp 120
ngtheta 120
END
QRST
QRST is a list keyword that is used to specify the options for the quantized-reactant-state
tunneling calculations. This option should only be used with unimolecular reactions. It
is described in Refs. 8 and 37 of Sect. 21. Be sure that MXWKB is large enough if you use
this (See Section 5.A.2. MXWKB must be greater than or equal to the total number of
energy levels.) STATES subkeyword determines the number of quantized reactant states to
be included in the tunneling calculations. The options are all (all possible states are
included in the calculation), 0 (only the vibrational ground state will be considered), 1
(only the ground state and the first vibrational states will be considered), etc. STQVIB
subkeyword determines the number of quantized reactant states to be included in
calculation of the reactant vibrational partition function. The options are all (all
possible states are included in the calculation), and samet (the number of states used for
calculating the reactant vibrational partition function is the same as the number of states
used for tunneling contributions). The valid options are defined below.
Option Description Default harmonic use the harmonic approximation to determine the energy on
levels of the reaction-path mode
harmwkb between the reactant and saddle point use the WKB off
approximation to find the energy levels but use the
harmonic potential as the effective potential to the left
of the reactant
symwkb use the WKB approximation to find the energy levels and off
assume that the effective potential is symmetric with
respect to the reactant mode the number of the selected vibrational reaction-path mode
required
srw the value of the reaction coordinate at the position of the required
reactant. The default unit is angstrom and it can also be
in bohr by specifying the keyword INPUNIT AU.
states the number of quantized reactant states to be included all
in the tunneling calculation stqvib the number of quantized reactant states to be included all
in the vibrational partition function calculation
Polyrate 222
Example: QRST
SYMWKB
STATES 5
MODE 3
SRW -2.42
STQVIB all
END
QUAD
QUAD is a list keyword that is used to specify the Gauss-Legendre quadrature points in
each segment used in computing the Boltzmann average (NQE) and theta integrals (NQTH)
in the tunneling calculations. The valid options are defined below.
Option Description Default
nqe number of Gauss–Legendre quadrature points in each 40
segment to be used for computing the Boltzmann average
in the tunneling calculations; allowed values are 2-7, 9,
10, 12, 15, 20, 30, and 40
nqth number of Gauss–Legendre quadrature points in each 40
segment to be used for computing the theta integrals in the
tunneling calculations; allowed values are 2-7, 9, 10,
12, 15, 20, 30, and 40 nsegboltz number of equal segments for integrals that average the 1
energy–dependent tunneling probabilities over a Boltzmann
distribution of energies
nsegtheta number of equal segments for the theta integrals 1
Example: QUAD
nqe 30
nqth 30
nsegboltz 2
nsegtheta 2
END
SCT (NOSCT)
SCT is a switch keyword that specifies that small–curvature tunneling calculations be
performed. Default is SCT.
Polyrate 223
SCTOPT
SCTOPT is a list keyword that is used to specify the method for interpolating the effective
mass for the small–curvature tunneling calculations. See Section 10.E. The default is
SPLINE. The valid options are defined below.
Option Description Default
lagrange n Lagrangian interpolation of order n is used to interpolate 4
µeff(s)
spline spline fit is used to interpolate µeff(s) on
Example: SCTOPT
lagrange 5
END
WIGNER
WIGNER is a switch keyword that specifies that the Wigner transmission coefficient be
computed. Default is on because it is inexpensive, but it is not a reliable method. In the
current version of POLYRATE, this option cannot be turned off.
ZCT (NOZCT)
ZCT is a switch keyword that specifies that zero–curvature tunneling calculations be
performed. Default is ZCT.
Polyrate 224
12.A.9. RATE section
The RATE section contains the keywords that control the rate constant calculations. This
section is not needed if rate constants are not desired. If this section is not included then
all defaults are ignored, and the default CVT and TST calculations are not performed. For
simplicity the keywords have been broken into three categories: basic, methods, and
print. This is only for clarity in the manual. The keywords in any of these three
categories can be used in any order. Also for simplicity the keywords in each category
have been labeled as either common or other. The keywords labeled common are those
that are found in most input files for a standard Polyrate run. This labeling is only
intended as an aid to the novice user. Again an alphabetical glossary of all the keywords
follows the three summary tables.
Polyrate 225
Basic:
Keyword Type Default Description
Common:
BOTHK switch on forward and reverse rate constants
EACT list not used activation energy calculation
REVKEXP variable 0 scale factor for reverse rates
SIGMAF variable 1 sym. factor for forward reaction
SIGMAR variable 1 sym. factor for reverse reaction
TEMP list see below temperatures for rate calculations
Others:
ANALYSIS list not used detailed analysis of TST/CVT ratio
EDGEOK switch on continue calculation even if Gmax is near end of grid
FORWARDK switch off forward rate constant only
GSPEC list not used special grid for G calculation
SMAX variable 1.0 ao max. s for special grid
SMIN variable -1.0 ao min. s for special grid
GTEMP list not used special grid for G calc. for given T
GTLOG switch off free energy of activation by logarithms
STATE variable therm thermal or state-selected rate constant
STATEOPT list thermal options for STATE keyword
SPTOPT list options for simple pert. theory
CORIOLIS switch off include Coriolis term
PRINT switch off extra data printed out
VPFEXP variable 0 scale factor for vibrational partition function
Polyrate 226
Methods:
Keyword Type Default Description
Common:
CVT switch on canonical VTST
Others:
TST switch on conventional transition state theory
MUVT switch off microcanonical VTST
MUVTOPT list options for VT
FIT variable gas53 primary and secondary fits
NITER variable 30 Gauss-Laguerre quadrature
PRENERGY variable 0 # of energies on the grid to print
SLOWER variable 0.0 lower limit of MEP for searching
SUPPER variable 0.0 upper limit of MEP for searching
CUS variable off canonical unified statistical model
US switch off unified statistical calculation
Polyrate 227
Print:
Keyword Type Default Description
Others:
PRDELG switch off print free energy curve
PRPART variable not used print reactant, product, and saddle point partition functions
PRVIB list not used region to print extra vib mode info
SX variable 0.0 s at beginning of desired region
SY variable 0.0 s at the end of desired region
Polyrate 228
Glossary of RATE keywords
ANALYSIS
ANALYSIS is a list keyword used to specify the temperatures (in Kelvin) at which a
detailed analysis of the conventional TST/CVT ratio is to be performed. The default is
not to do a detailed analysis at any temperature. (Note: the rate constant must be
computed at all temperatures on this list; see the TEMP keyword.)
Example: ANALYSIS
298.
400.
800.
END
BOTHK (NOBOTHK)
BOTHK is a switch keyword that specifies that both the forward and reverse rate constants
and the equilibrium constant are to be calculated. If NOBOTHK is specified no rate
constants are computed; use FORWARDK if only the forward rate constant is desired. The
default is BOTHK. (See REVKEXP for scaling the output for the reverse rate constant.)
CUS (NOCUS)
CUS is a variable keyword that specifies that rate constants should be calculated with the
canonical unified statistical model. See Ref. 51 in Sect. 22. The input argument of this
keyword indicates the maximum number of local maxima in the free energy of activation
vs. reaction coordinate profiles that should be included at each temperature. If the
number of local maxima that are found is less than this argument, then all maxima are
used. The CUS calculations will also include the lowest local minimum between any pair
of included local maxim. When the argument of CUS equals 1, the CUS result is exactly
the same as CVT. The default is NOCUS.
Example: CUS 2
CVT (NOCVT)
CVT is a switch keyword that specifies that generalized transition state theory and
canonical variational theory rate constants be calculated. The default is CVT. If NOCVT is
specified and NOTST is not specified, rate constants will be calculated but only at the
conventional-TST level. In this case, the calculations are carried out in subprogram
TSRATE (as opposed to RATE or GIVTST). TSRATE does not include anharmonicity.
Polyrate 229
EACT
EACT is a list keyword used to specify the pairs of temperatures (in Kelvin) for which to
compute Arrhenius activation energies (maximum of 10 pairs) from the calculated rate
constants. Each line should first give the lower temperature and then the upper
temperature for the pair. The default is not to compute any activation energies. (Note:
the rate constant must be computed at all temperatures in this list; see the TEMP keyword.)
Example: EACT
298. 400.
400. 600.
END
EDGEOK (NOEDGEOK)
EDGEOK is a switch keyword that specifies that the calculation be continued even if Va or
GICVT is near an end point, i.e., even if the grid does not appear wide enough to find
variational transition states. The default is EDGEOK.
FORWARDK (NOFORWARDK)
FORWARDK is a switch keyword that specifies that only the forward rate constant be
calculated. If FORWARDK is specified, equilibrium constants will not be computed. The
default is NOFORWARDK.
GSPEC
GSPEC is a list keyword that is used to specify that the generalized free energy of
activation profile only be computed for the range SMIN s SMAX for all temperatures.
The default is to compute the free energy curve over the entire range of s. The default
unit is angstroms and it can also be in bohr by specifying the keyword INPUNIT AU. The
defaults for the options are SMAX = 1 ao and SMIN = -1 ao.
Example: GSPEC
SMAX 1.50
SMIN -0.05
END
GTEMP
GTEMP is a list keyword that is used to specify that the generalized free energy of
activation profile be computed over a different range of s for each temperature. Each
Polyrate 230
entry in the list should contain the temperature in Kelvin and then SMAX and SMIN (in
bohr) for that temperature. The default is to compute the free energy curve over the
entire range of s. The default unit is angstroms and it can also be in bohr by specifying
the keyword INPUNIT AU. The defaults for the options are SMAX = 1 ao and SMIN = -1 ao.
Example: GTEMP
298. 1.50 -0.10
400. 1.00 -0.25
END
GTLOG (NOGTLOG)
GTLOG is a switch keyword that specifies that the generalized free energy of activation
should be calculated by using the logarithms of the vibrational partition functions. This
type of calculation is preferred when the vibrational partition function has an extremely
small value (as may be the case for very low temperatures and/or for very big systems
because we put the zero of energy for the partition coefficient at the lowest value of the
potential rather that at the zero point energy). The default is NOGTLOG.
MUVT (NOMUVT)
MUVT is a switch keyword that specifies that VT rate constants should be calculated.
The default is NOMUVT if US and MUVTOPT are off, and the default is MUVT if US is on or
MUVTOPT is given.
Polyrate 231
MUVTOPT (NOMUVTOPT)
MUVTOPT is a list keyword that is used to set options for the VT calculation. If
MUVTOPT is given then it is assumed that the VT calculation is desired and the default
for MUVT becomes on. The valid options are defined below.
Option Description Default
niter number of Gauss-Laguerre quad. pts. for computing VT rate 30
constants
prenergy number of energies on the grid to be printed out; PRENERGY must 0
be £ min 6,niter
slower lower limit, respectively, of the region of the MEP over 0.0
which the GT minimum of NVT will be searched for. (This is
only specified if one wishes to limit the search. Leave set to the
default of zero to search over the entire s range.) The default
unit is angstroms and it can also be in bohr by specifying the
keyword INPUNIT AU.
supper upper limit, of the region of the MEP over which the GT
minimum of N will be searched 0.0
for. (This is only specified if one wishes to limit the search.
Leave set to the default of zero to search the entire s range.)
The default unit is angstroms and it can also be in bohr by
specifying the keyword INPUNIT AU. fit variable that specifies the degree of the primary and secondary gas53
fits. The allowed values are given below. For a gas-phase reaction,
gas53 is the recommended value, and for a reaction at a gas-solid
interface, gsolid13 is recommended. Sometimes there is a numerical
problem with the 5-point fit; in such a case it is recommended to use
gas31 rather than gas53.
value primary secondary phase
gas53 5 3 gas
gas15 1 5 gas
gas35 3 5 gas
gas31 3 1 gas
gas13 1 3 gas
gsolid13 1 3 gas-solid interface
gsolid15 1 5 gas-solid interface
gsolid31 3 1 gas-solid interface
gsolid53 5 3 gas-solid interface
Example: MUVTOPT
niter 40
END
Polyrate 232
PRDELG (NOPRDELG)
PRDELG is a switch keyword that specifies that G(T,s) be printed to fu6. Default is
NOPRDELG.
PRPART (NOPRPART)
PRPART is a variable keyword. Its argument specifies that the reactant and product (rp)
partition functions, the saddle point (t) partition functions, or the reactant, product, and
saddle point (rpt) partition functions should be printed to fu6. When the reactant
partition function is printed for a gas-phase unimolecular reaction the internal free energy
of reactant is also printed. The default is not to print any partition functions or free
energies at the stationary points.
Example: PRPART rp
PRVIB
PRVIB is a list keyword that is used to specify the initial and final s values, with keywords
sx and sy respectively, that delineate a region for which extra vibrational mode and Qvib
information be printed to fu6. The default is no extra printing. The default unit is
angstroms and it can also be in bohr by specifying the keyword INPUNIT AU.
Example: PRVIB
SX 0.0
SY 0.6
END
REVKEXP
REVKEXP is a variable keyword whose argument specifies the value n in the scale factor
10-n for the reverse rate constant. The final rate will be calculated in units of 10-n cm3
molecule-1 s-1 if there are two products or in units of 10-n s-1 if there is one product.
Default is n = 0, i.e., a scale factor of 1.
Example: REVKEXP 10
Polyrate 233
SIGMAF
SIGMAF is a variable keyword whose argument specifies the number of equivalent ways
for forming the GTS for the forward reaction. The default value is 1.
Example: SIMGAF 1
SIGMAR
SIGMAR is a variable keyword whose argument specifies the number of equivalent ways
for forming the GTS for the reverse reaction. The default value is 1.
Example: SIMGAR 1
STATE
STATE is a variable keyword whose argument specifies if this is to be a thermal or state–
selected rate constant calculation. The default is therm. The valid arguments are:
Option Description
therm thermal run
adiab adiabatic state-selected; STATEOPT is required
diab x diabatic state-selected; x is the value of the reaction
coordinate at which the adiabatic/diabatic switch is made;
STATEOPT is required
Example: STATE adiab
Polyrate 234
STATEOPT
STATEOPT is a list keyword that is used to specify how each mode in each reactant,
product, and transition state is to be treated. By default each mode is treated thermally.
The user needs to specify each mode explicitly that is to be restricted to the ground state
or first excited state as shown below. Each input line in the list requires:
reatyp nmode modtyp
The allowed values of the variable reatyp are:
Value Description
react1 reactant #1
react2 reactant #2
prod1 product #1
prod2 product #2
ts transition state and along the reaction path
switts reaction path after the adiabatic/diabatic switch (see
STATE)
nmode is an integer specifying the vibrational mode number
The allowed values of the variable modtyp are:
Value Description
thermal mode is thermal (default)
ground mode is restricted to the ground state
first mode is restricted to the first excited state
Example: STATEOPT
react1 1 ground
react2 1 first
prod1 1 thermal
prod1 2 ground
prod1 3 first
ts 4 ground
ts 5 first
switts 4 first
switts 5 ground
END
Polyrate 235
TEMP
TEMP is a list keyword used to specify the temperatures (in Kelvin) at which rate
constants be computed. Unless NOBOTHK or FORWARDK is selected the equilibrium
constants will also be calculated at these temperatures. The default is to compute the rate
constants at 7 temperatures: 200, 300, 400, 600, 1000, 1500, and 2400.
Example: TEMP
298.
400.
600.
800.
END
TST (NOTST)
TST is a switch keyword that specifies that the conventional transition state theory rate
constants be calculated. The default of TST is on. If any other rate constants are
calculated, i.e., CVT, ICVT, US, or VT, then the conventional rate constants will
automatically be calculated (NOTST will have no effect) except when VRC is turned on
US (NOUS)
US is a switch keyword that specifies that unified statistical rate constants be calculated.
If US is on, then MUVT is automatically turned on. The default of US is off, which is the
same as specifying NOUS.
VPFEXP
VPFEXP is a variable keyword that that specifies that the total vibrational partition
functions be scaled by 10n where n is the argument. The default is no scaling.
Example:
VPFEXP 2
Polyrate 236
12.B. General description of file fu29 input
File fu29 is only needed if IVTST0 or IVTST1 is specified in the GENERAL section of the
unit fu5 input. This unit contains input data for IVTST rate calculations. The first section
of this input file must be *IVTST. All input sections must start with the section name
preceded by an “*”, and must end with an END line (a line containing “end”). Keywords
and input data for each section are discussed further in the rest of this subsection. Sample
inputs can be found in several test runs described in Section 16.
Section Name Description
*E1GEOM Cartesian coordinates of the extra point on the MEP
*E1GRAD Cartesian gradient vector of the extra point on the MEP
*E1HESS Cartesian Hessian of the extra point on the MEP
*IVTST general data for IVTST calculations (must come first)
*P1FREQ frequencies of the 1st product
*P2FREQ frequencies of the 2nd product
*P1HESS Cartesian Hessian of the 1st product
*P2HESS Cartesian Hessian of the 2nd product
*R1FREQ frequencies of the 1st reactant
*R2FREQ frequencies of the 2nd reactant
*R1HESS Cartesian Hessian of the 1st reactant
*R2HESS Cartesian Hessian of the 2nd reactant
*TSHESS Cartesian Hessian of the saddle point
*TSFREQ frequencies of the saddle point
When IVTST0 is specified, the user can choose between giving the Hessian or the
frequencies for the stationary points (reactants, saddle point and products) according to
the kind of information available for the system. When running an IVTST1 calculation
the use of Hessians for the stationary and extra points is required, since this information
is needed in order to calculate the SCT transmission factors.
Polyrate 237
12.B.1. E1GEOM Section
The E1GEOM section of the file fu29 input is used to give the Cartesian coordinates of the
extra point on the MEP. This section is only needed for first-order IVTST calculations.
Example: *E1GEOM
0.000000 0.000000 0.000000
0.456364 1.749560 0.000000
1.808100 0.000000 0.000000
END
12.B.2. E1GRAD Section
The E1GRAD section of the file fu29 input is used to give the Cartesian gradient vector of
the extra point on the MEP. This section is only needed for first-order IVTST
calculations.
Example: *E1GRAD
0.000000 0.000000 0.000000
0.056364 0.009560 0.000000
0.008100 0.000000 0.000000
END
12.B.3. E1HESS, P1HESS, P2HESS, R1HESS, R2HESS, and TSHESS sections
The E1HESS, P1HESS, P2HESS, R1HESS, R2HESS, and TSHESS sections of file fu29 input are
used to give the Cartesian Hessian matrix of the extra point on the MEP, products,
reactants, and the transition state in packed form, respectively. The E1HESS section is
only needed for first-order IVTST calculations.
Example: *E1HESS
0.000000
0.056364 0.009560
0.008100 0.000000 0.000000
0.008100 0.000000 0.000000 0.080100
0.008100 0.000000 0.000000 0.080100 0.080100
0.008100 0.000000 0.000000 0.080100 0.080100
0.080100
END
Polyrate 238
12.B.4. IVTST Section
The IVTST section of the file fu29 input is used to give general data for IVTST
calculations. The table below lists all valid subkeywords for the IVTST section. A
detailed explanation of each keyword is given alphabetically in the glossary below.
Keyword Type Default Description
BARRI variable required classical barrier height in kcal/mol
DELTAE variable required classical energy of the products in kcal/mol
DELEX1 variable not used the classical energy of the extra point in kcal/mol (only needed for the IVTST1)
PRINT switch 0 output control
SEX1 variable not used the reaction coordinate at the extra point in atomic units (only needed IVTST1)
UNITS switch 0 units for geometry, gradient, and Hessian matrix
Glossary of IVTST keywords
BARRI
BARRI is a keyword that specifies the classical barrier height in kcal/mol. In case a
conversion of units is required for obtaining this value in kcal/mol, the conversion factor
used should be the same as that internally employed by Polyrate as specified in the
percon.inc file.
Example: BARRI 5.0
Polyrate 239
DELTAE
DELTAE is a keyword that specifies the classical energy of the products relative to the
classical energy of the reactants in kcal/mol. This is a required keyword. In case a
conversion of units is required for obtaining this value in kcal/mol, the conversion factor
used should be the same as that internally employed by Polyrate as specified in the
percon.inc file.
Example: DELTAE -5.0
DELEX1
DELEX1 is a keyword that specifies the classical energy of the extra point relative to the
classical energy of the reactants in kcal/mol. This keyword is only needed for first-order
IVTST calculations.
Example: DELEX1 -4.4
PRINT is a keyword for output control: 0—normal (default), 1—debug.
Example: PRINT 1
SEX1
SEX1 is a keyword that specifies the reaction coordinate at the extra point in bohr. This
keyword is only needed for first-order IVTST calculations.
Example: SEX1 0.1
UNITS
UNITS is a keyword that specifies the units for the geometry, gradients and Hessian
matrix: UNITS = 0: The geometry will be in bohrs, and both the gradients, and the
Hessian matrix will be in mass-scaled atomic units (default). UNITS = 1: The geometry
will be in mass-scaled Å, and both the gradient vectors and the Hessian matrix will be in
non-mass-scaled atomic units.
Example: UNITS 0
Polyrate 240
12.B.5. P1FREQ, P2FREQ, R1FREQ, R2FREQ, and TSFREQ sections
The P1FREQ, P2FREQ, R1FREQ, R2FREQ, and TSFREQ sections of the file fu29 input are used
to give the frequencies (in cm–1
) of the product and reactant molecules and the saddle
point, respectively. The imaginary frequency of the saddle point must be the last input
value in the TSFREQ section.
Example: *R1FREQ
2000.0 1000.0
END
Polyrate 241
12.C. General description of file fu30 input
File fu30 contains the information typically obtained from electronic structure
calculations which is required for performing a direct dynamics calculation (see Section 9
for a detailed description of this capability). This option is selected by setting the
keyword POTENTIAL in the ENERGETICS section equal to unit30.
File fu30 is organized in the following way: 1) a one-line title; 2) 2 lines with numerical
options for routing and output; and 3) several blocks of data containing the specific
information provided for each point on the reaction path according to the options selected
(s, V, frequency matching data, Cartesian coordinates, gradient, frequencies or Hessian
matrix, anharmonicity data, curvature component data, etc.).
The user should be aware that gradients provided in the fu30 file must correspond to
structures that have not been arbitrarily reoriented along the reaction path in order to
obtain meaningful results in the calculation of the curvature components BmF. See
Section 9 for a fuller discussion of this issue.
A record-by-record description (where a record is one or more lines) of the structure of
the FORTRAN unit fu30 follows. If the keyword POTENTIAL = unit30, Polyrate can
be used with the dummy potential energy surface file provided, dumpot.f, since the
potential routines SURF and SETUP will not be called.
Record Format
(Records 1 and 2 are read in subprogram RPHSET)
1 One-line title (80A1)
2 Routing and output options (LOPT(I), I = 1, 40) (*)
LOPT(1) LEVEL OF PRINT
0, print out only titles and options
= 1, also print out summary
= 2, also echo input as it is read
= 3, also print out intermediate information about
fitting exponential functions and print
out interpolated results each time
RPHINT is called
Polyrate 242
4, also print out debugging information in
exponential fitting
LOPT(2) MAXIMUM NUMBER OF POINTS USED IN LAGRANGE
INTERPOLATION IN THE PROCEDURE OF SUBSECTION
9.C.
= –1, use IVTST-M for interpolating. See Sect.
9.C.
Note: When using file fu30, the user cannot select any options for the IVTST-M
calculation; it will be performed according to the default options, and the number of
gradient and Hessian points have to be the same and equal to NPTS (see below).
Therefore, only IVTST-M-NPTS/NPTS calculations are allowed. The curvature
components will be interpolated using a value of 3 for the exponent in the mapping
function. For unimolecular reactions or reactions with wells, a cubic polynomial
fitting to V is done previous to its spline fitting, taking a step of 0.01 a0 along the
lowest frequency mode for performing this fitting. The only way to change any of
these options or to use a different number of gradient and Hessian points is by using
the fu31 input file, which is specifically designed for IVTST-M calculations.
LOPT(3) OPTIONS FOR COORDINATES (X) AND GRADIENTS (DX)
-2, X in mass-scaled Cartesians, DX in
unscaled Cartesians
= -1, X in unscaled Cartesians, DX in mass–
scaled Cartesians
= 0, X and DX in unscaled Cartesians
= 1, X and DX in mass-scaled Cartesians
= 99, X in unscaled Cartesians, -DX in mass-
scaled Cartesians
= 100, X in unscaled Cartesians, -DX in
unscaled Cartesians
Note: DX denotes the gradient, and -DX denotes the negative of the gradient which
is the force. For dynamics calculations in Cartesian coordinates, the normalized
gradients (or forces) can be used without any effects on the results. However,
unnormalized gradients have to be used for the curvilinear option. Notice the
‘Cartesian Forces’ from GAUSSIAN formatted check point output file are actually
the Cartesian gradient components.
LOPT(4) OPTIONS FOR FREQUENCY OR HESSIAN MATRIX INPUT
There are three issues:
Polyrate 243
(1) Are the frequencies read in from unit fu30, or are they
obtained by diagonalizing the Hessian matrix F or the
projected Hessian FP?
(2) If the frequencies are calculated from the Hessian, how is F
read in, in packed (triangular) form, in packed form with full
lines, or in unpacked (full matrix) form?
(3) What coordinate system was used in computing F?
LOPT(4) (1) (2) (3)
-2, diagonalization packed mass-scaled coordinates
= -1, diagonalization packed unscaled coordinates
= 0, frequencies are
read
= 1, diagonalization full matrix unscaled coordinates
= 2, diagonalization full matrix mass-scaled coordinates
Notes: (1) If LOPT(4) 0, the choice of coordinates (mass-scaled or not) must be
consistent with LOPT(3).
(2) If the Hessian is read, the code assumes it is the non-projected Hessian.
(3) Packed full lines means 5 elements per line; whereas packed triangular
means F(1,1) on first line, F(2,1) and F(2,2) on second line, etc.
LOPT(5) ANHARMONICITY INPUT
0, no anharmonicity data read
= 1, read the third derivatives k3 with respect to the
normal coordinates at each grid point
2, also read the fourth derivatives k4 with respect
to the normal coordinates at each grid point
LOPT(6) OPTIONS FOR CURVATURE COMPONENT BmF INPUT
0, BmF are set to zero everywhere
= 1, BmF are read directly
= 2, BmF are computed. Derivative of the gradient
with respect to s is obtained from a quadratic fit
of the gradient at three points on the basic input
grid (defined in Section 9.C), with the middle
point being the current point on the Hessian
grid.
= 3, BmF are computed. Derivative of the gradient is
computed by one-sided finite difference, using
the gradient on the basic input grid and a
Polyrate 244
gradient input at one extra point near the basic
input grid point.
4, BmF are computed. Derivative of the gradient is
computed from a quadratic fit obtained using
the gradient on the basic input grid and
gradients input at an extra point on each side of
the basic input grid point.
Note: For LOPT(6) > 1, BmF are computed and require the coefficient matrix
from the diagonalization of the Hessian matrix. Therefore, LOPT(4) must be
nonzero if LOPT(6) > 1.
LOPT(7)-LOPT(40): Not used in the present version of POLYRATE.
Loop over records 3 through 14 for each reactant species and then for each product
species. Records 3-25 are read in subprogram RPHRD2.
3 One-line title (80A1)
4 S, V (*)
S = value of s in bohrs at reactant (or product). This only has
meaning for a unimolecular and/or association reaction, for which s
is finite at the reactant and/or product; otherwise S is ignored.
V = potential (in atomic units) at reactants (or products).
For an atomic reactant or product, skip records 5 through 14, add a blank line after
record 4, and then continue with the next species.
5 (IFREQ(I),I = 1, NFREQ) (*)
IFREQ = indices for reordering frequencies, anharmonicities, and
curvature components in the interpolation table for the reactant or
product species, in order to make the ordering consistent with that at
the saddle point and/or along the MEP.
Note: Index 1 corresponds to the largest frequency at the saddle
point, index 2 to the second largest frequency, and so on. The
imaginary frequency is not included in this ordering.
Note that this matching is not necessary if you are just calculating
conventional TST reaction rates.
NFREQ is the number of bound vibrational modes for the species.
Polyrate 245
For a Morse diatom reactant or product, read record 6; otherwise go to record 7.
6 SGN
SGN = sign used to multiply the third derivative of the diatomic
potential. This can be used to make the sign of the third derivative
of this mode in the asymptotic reactant or product region match up
with the correlating mode in the interaction region. This ensures a
smooth extrapolation into the asymptotic region.
For a Morse diatom reactant or product, skip records 7 through 14. If LOPT(4) = 0
(frequencies directly input), skip records 7 and 8.
7 One-line title (80A1)
8 N records of (F(I,J),J = 1, JF) N records of (*)
F = Hessian matrix (in atomic units) for the reactant or product
species. Second derivatives are with respect to Cartesian
coordinates; LOPT(4) determines whether the coordinates are mass-
scaled or not. JF = N for LOPT(4) > 0 and JF = I for LOPT(4) < 0,
where N = 3*NRATOM, NRATOM = number of atoms in the species,
and I indexes the N records in this set (I = 1,..., N).
If LOPT(4) 0, skip records 9 and 10.
9 One-line title (80A1)
10 (FREQ(I), I = 1, NFREQ) (*)
FREQ = vibrational frequencies (in atomic units) for the reactant
or product species.
If LOPT(5) < 1 (no anharmonicity), skip records 11 through 14.
11 One-line title (80A1)
12 (XK3(I), I = 1, NFREQ) (*)
XK3 = third derivatives of V with respect to motion along the
normal coordinates for the reactant or product species.
If LOPT(5) < 2 (just third derivatives), skip records 13 and 14.
Polyrate 246
13 One-line title (80A1)
14 (XK4(I), I = 1, NFREQ) (*)
XK4 = fourth derivatives of V with respect to motion along the normal
coordinates for the reactant or product species.
After each reactant or product species except for the last product, go back to record 3.
After the last product, go to the next record.
If there is no saddle point, skip records 15 through 27.
15 One-line title (80A1)
16 S, V (*)
S = a dummy quantity and is ignored.
V = potential (in atomic units) at the saddle point.
17 (IFREQ(I), I = 1, NFREQ) (*)
These quantities are the same as in record 5, but now they refer to
the bound vibrational modes of the saddle point. NFREQ is now
the number of bound vibrational modes of the saddle point.
If LOPT(4) = 0, skip records 18 and 19.
18 One-line title (80A1)
19 N3 records of (F(I,J), J = 1, JF) N3 records of (*)
These quantities are the same as in record 8, but now they refer to
the saddle point. JF = N3 for LOPT(4) > 0 and JF = I for LOPT(4) <
0, where I indexes the N3 records in this set (I = 1,...., N3), and
where N3 = 3*NATOM, NATOM = number of atoms in the system.
If LOPT(4) 0, skip records 20 and 21.
20 One-line title (80A1)
21 (FREQ(I), I = 1, NFREQ) (*)
These quantities are the same as in record 10, but now they refer to
the bound vibrational modes of the saddle point.
Polyrate 247
If LOPT(5) < 1 (no anharmonicity), skip records 22 through 25.
22 One-line title (80A1)
23 (XK3(I), I = 1, NFREQ) (*)
These quantities are the same as in record 12, but now they refer to
the bound vibrational modes of the saddle point.
If LOPT(5) < 2 (just third derivatives), skip records 24 and 25.
24 One-line title (80A1)
25 (XK4(I), I = 1, NFREQ) (*)
These quantities are the same as in record 14, but now they refer to
the bound vibrational modes of the saddle point.
If LOPT(4) 0, skip records 26 and 27.
Records 26-31 are read in subprogram RPHRD1.
26 One-line title (80A1)
27 WSTAR (*)
WSTAR = absolute value of the imaginary frequency at the saddle point.
If the reaction path is calculated, read records 28 to 63.
28 One-line title (80A1)
29 NPTS (*)
NPTS = number of s points along the MEP (not including the saddle point) at
which reaction-path Hamiltonian data is to be read (maximum of 200).
Unless only TST reaction rates are calculated, file fu30 must contain a
minimum of one point on each side of the saddle point. Unless NEXTPT is on,
these points must be arranged in order of increasing S.
Loop over records 30 through 52 NPTS times, from the lowest value of s to the highest
value of s. Records 30-50 are read in subprogram RPHRD2.
30 One-line title (80A1)
31 S, V (*)
Polyrate 248
S = value of s (in bohr) at the grid location along the MEP.
V = potential (in hartrees) at s on the MEP.
32 One-line title (80A1)
33 (X(I), I = 1, N3) (*)
X = Cartesian coordinates of the GTS at s on the MEP.
N3 = 3*(number of atoms in the total system). Ordering is the same
as specified in the ATOM keyword of the FORTRAN unit fu5 data.
Note: LOPT(3) determines whether the coordinates are mass-scaled
or not.
34 One-line title (80A1)
35 (DX(I), I = 1, N3) (*)
DX = gradient vector (in atomic units) at s along the MEP. DX can
be the vector of derivatives of the potential with respect to the
Cartesian coordinates or it can be normalized. LOPT(3) determines
whether the coordinates are mass-scaled or not. Ordering is the
same as for X(I) in record 33.
Note: Some electronic structure codes print the force rather than
the gradient. Recall that the force is the negative of the gradient.
If LOPT(6) 2, skip records 36 through 41.
36 One-line title (80A1)
37 SB(1) (*)
SB(1) = value of s (in bohr) at a location along the MEP close to the
current grid point.
38 (DX(I), I = 1, N3) (*)
These quantities are the same as in record 35, but now they refer to the
location SB(1) on the MEP.
If LOPT(6) 3, skip records 30 through 41.
39 One-line title (80A1)
Polyrate 249
40 SB(2) (*)
SB(2) = value of s (in bohr) at another location along the MEP close
to the current grid point.
41 (DX(I), I = 1, N3) (*)
These quantities are the same as in record 35, but now they refer to
the location SB(2) on the MEP.
42 (IFREQ(I), I = 1, NFREQ) (*)
These quantities are the same as in record 17, but now they refer to
the bound generalized normal modes of the current grid point along
the MEP.
If LOPT(4) = 0, skip records 43 and 44.
43 One-line title (80A1)
44 N3 records of (F(I,J), J = 1, JF) (*)
These quantities are the same as in record 19, but now they refer to
the current grid point along the MEP.
If LOPT(4) 0, skip records 45 and 46.
45 One-line title (80A1)
46 (FREQ(I), I = 1, NFREQ) (*)
These quantities are the same as in record 21, but now they refer to the
current grid point along the MEP.
If LOPT(5) < 1 (no anharmonicity), skip records 47 through 50.
47 One-line title (80A1)
48 (XK3(I), I = 1, NFREQ) (*)
These quantities are the same as in record 23, but now they refer to
the current grid point along the MEP.
If LOPT(5) < 2 (just third derivatives), skip records 51 and 52.
Polyrate 250
49 One-line title (80A1)
50 (XK4(I), I = 1, NFREQ) (*)
These quantities are the same as in record 25, but now they refer to the
current grid point along the MEP.
If LOPT(6) = 1 (BmF are read), read records 51 and 52.
Records 51-63 are read in RPHRD1.
51 One-line title (80A1)
52 (BFS(I), I = 1, NFREQ) (*)
BFS = reaction-path curvature components (in atomic units) at the
current grid point along the MEP.
Return to record 30 until records 30 through 52 have been read NPTS times.
Polyrate 251
12.D. General description of file fu31 input
This file is only needed if the POTENTIAL keyword of the ENERGETICS section of file fu5 is
equal to unit31. The input is in free format keyword style and is composed of several
sections. When unit31 is used, the code always uses the IVTST-M algorithm.
12.D.1. Section descriptions
Section Name Description
*GENERAL general data such as options for input and IVTST-M
*REACT1 information for the first reactant
*REACT2 information for the second reactant (if any)
*PROD1 information for the first product
*PROD2 information for the second product (if any)
*WELLR information for the well on the reactant side (if any)
*WELLP information for the well on the product side (if any)
*SADDLE information for the saddle point
*POINT information for a point along the MEP
Each section must appear once and only once except POINT, which has to appear at least
twice (since IVTST-M is not defined for less than one point on each side of the reaction
path). The POINT section should be repeated once for each of the nonstationary points
along the MEP. A saddle point is also required for carrying out an IVTST-M calculation.
Therefore, the fu31 input file cannot be used for reactions without a saddle point.
The program is insensitive to the order in which the points are entered. This is one of the
main differences between the fu31 input file and the fu30 and fu40 files. This allows us
to use an fu31 file written by means of the writefu31 option for the RESTART
keyword in the GENERAL section of the fu5 input file without any change. Another
difference is that Hessians are not required at each point; since the calculation of the
Polyrate 252
reaction path always gives a value of the reaction coordinate, s, the energy, geometry, and
gradients, this information is required, but the Hessian information is not. This way, the
user can take advantage of the information calculated for points between two Hessian
points.
Since the IVTST-M calculation is always based on frequencies ordered in canonical
order, no frequency indexes are required. Moreover, since anharmonicity is not
supported for IVTST-M calculations, in the current version of POLYRATE, no anharmonic
data is allowed. From all other points of view, the fu31 input file is very similar to a fu30
or fu40 input file.
Polyrate 253
12.D.2 GENERAL section
Keyword Type Default Description
GEOM list no changes change defaults for reading geometries
GRADS list no changes change defaults for reading gradients
HESSIAN list no changes change defaults for reading Hessians
INTMUEFF switch off interpolation of the exponent in the effective tunneling mass
KIES switch off recalculation of the s values
Polyrate 254
Glossary of GENERAL keywords
GEOM
GEOM is a list keyword for selecting the units of the geometries input in the fu31 file. The
units are completely defined by a combination of two keywords; thus, if we want to input
the mass-scaled geometries in angstroms we will have to select both ms and ang. If one
of the options is not given, the default value is assumed.
Option Definition ang Geometries are given in Å.
au Geometries are given in atomic units (default).
ms Geometries are given in mass-scaled Cartesian coordinates.
uns Geometries are given in unscaled Cartesian coordinates (default).
Example: GEOM
ang
ms
END
GRADS
GRADS is a list keyword for selecting the units of the gradients (or forces) input in the
fu31 file. The units are completely defined by a combination of three keywords.
Option Definition
ang Gradients are given in Å.
au Gradients are given in atomic units (default).
ms Gradients are given in mass-scaled Cartesian coordinates.
uns Gradients are given in unscaled Cartesian coordinates
(default). forces Forces are given; the gradients are obtained from them.
grads Gradients are given (default).
Example: GRADS
ang
uns
forces
END
Polyrate 255
HESSIAN
HESSIAN is a list keyword for selecting the units of the Hessian matrices input in the fu31
file. The units are completely defined by a combination of three keywords.
Option Definition
ang Gradients are given in Å.
au Gradients are given in atomic units (default).
ms Gradients are given in mass-scaled Cartesian coordinates.
uns Gradients are given in unscaled Cartesian coordinates (default).
full Full Hessian matrices are given.
packed Packed Hessian matrices are given (default).
Example: HESSIAN
full
END
If packed is selected, the lower triangular elements of F should be listed in order such
that F P i i jij = - +( ( ) )12
1 , where P(k) is element k of the input list and Fij is the
element of F in row i and column j. The number of elements listed per line is arbitrary.
Examples of both input forms for a 6 x 6 matrix is shown below:
Full matrix - example 1
F11 F12 F13 F14 F15 F16
F21 F22 F23 F24 F25 F26
F31 F32 F33 F34 F35 F36
F41 F42 F43 F44 F45 F46
F51 F52 F53 F54 F55 F56
F61 F62 F63 F64 F65 F66
Full matrix - example 2
F11 F12 F13 F14 F15 F16 F21 F22 F23
F24 F25 F26 F31 F32 F33 F34 F35 F36
F41 F42 F43 F44 F45 F46 F51 F52 F53
F54 F55 F56 F61 F62 F63 F64 F65 F66
Packed matrix - example 1
Polyrate 256
F11
F21 F22
F31 F32 F33
F41 F42 F43 F44
F51 F52 F53 F54 F55
F61 F62 F63 F64 F65 F66
Packed matrix - example 2
F11 F21 F22 F31 F32 F33
F41 F42 F43 F44 F51 F52
F53 F54 F55 F61 F62 F63
F64 F65 F66
The order of the coordinates is explained in Section 12.E.1.
Note that GAUSSIAN94 writes the packed Hessian matrix in a slightly different way in the
standard output file, but the Hessian in the formatted checkpoint file (requested by their
FormCheck keyword) is in precisely the packed form accepted by Polyrate and so is
convenient for copying and pasting into Polyrate fu40 files.
Note that the exact F matrix is symmetric, but due to finite precision in computations, the
actual matrix one has to input is usually nonsymmetric. If one inputs a nonsymmetric full
matrix, the code uses the unsymmetric matrix. If a user wants the code to use a
symmetric matrix, we recommend taking an arithmetic average of Fij and Fji for the
resulting symmetrized elements in packed form.
INTMUEFF (NOINTMUEFF)
The interpolation of the effective mass for CD-SCSAG tunneling can be done in two
ways in an IVTST-M calculation: by means of the interpolation of the curvature
components and evaluation of the effective mass, or by means of the direct interpolation
of the effective mass, specifically, of the term inside the exponential of the equation 16 in
Ref. IVTST-M. The latter option can be selected by means of the INTMUEFF switch
keyword, but the former option (NOINTMUEFF) is recommended and it is set as the default
option.
Polyrate 257
KIES (NOKIES)
In a calculation of kinetic isotope effects the values of the reaction coordinate, s,
calculated for one isotopomer are not valid for another isotopomer, since the values of s
are defined in a mass-scaled space. The KIES keyword allows the calculation of the
kinetic-isotope-effects-specific values of s. These values are calculated as the straight
line between two consecutive points in the isotope-specific mass-scaled space.
Therefore, if the KIES keyword is on, the values of s included in the fu31 input file will
only be used for ordering the points along the reaction path according to the standard
procedure: first the points with negative s, then the saddle point, and then the points with
positive s, ordered in increasing value of s. The geometries in file fu31 must be given in
unscaled coordinates (GEOM = uns). Nevertheless, if the calculation of new values of s
gives place to an permutation in the position of two points (which will not occur as a
consequence of just a change in an atomic mass) the program will not detect it, and the
interpolation will probably fail. The default is off (NOKIES) and its use is only
recommended for a KIE's calculation with RODS using a the reaction path calculated
with a different isotope.
Polyrate 258
12.D.3. REACT1, REACT2, PROD1, PROD2, WELLR, WELLP, and SADDLE
sections
Keyword Type Default Description
VMEP variable (see Glossary) value of VMEP(s)
SMEP variable (see Glossary) value of s
GEOM list (see Glossary) geometries
GRADS list (see Glossary) gradients
HESSIAN list (see Glossary) Hessians
ENERXN variable (see Glossary) reaction energy
ENERSAD variable (see Glossary) barrier height
ENEWELLR variable (see Glossary) energy of the well on the reactant side of the reaction-path
ENEWELLP variable (see Glossary) energy of the well on the product side of the reaction-path
Polyrate 259
Glossary of REACT1, REACT2, PROD1, PROD2, WELLR, WELLP, and SADDLE keywords
ENERSAD
ENERSAD is a variable keyword that indicates the value of the barrier height, in atomic
units (measured by taking the zero of energy at reactants). Its only acceptable position is
in the SADDLE section, where it is required.
ENERWELLR
ENERWELLR is a variable keyword that indicates the energy of the well on the reactant
side of the reaction path, in atomic units (measured by taking the zero of energy at
reactants). Its only acceptable position is in the WELLR section.
ENERWELLP
ENERWELLP is a variable keyword that indicates the energy of the well on the product side
of the reaction path, in atomic units (measured by taking the zero of energy at reactants).
Its only acceptable position is in the WELLP section.
ENERXN
ENERXN is a variable keyword that indicates the reaction endoergicity, in atomic units
(measured by taking the zero of energy at reactants). Its only acceptable positions are the
PROD2 section for reactions with two products, and the PROD1 section for reactions with
one product.
GEOM
GEOM is a list keyword that specifies the Cartesian coordinates at the current grid point.
Its only acceptable position is the POINT sections, where it is required; the geometries for
the stationary points are read from the fu5 input file.
GRADS
GRADS is a list keyword that specifies the Cartesian gradients (or forces) at the current
grid point. Its only acceptable position is the POINT sections, where it is required, since
the gradients for the stationary points are assumed to be zero.
HESS
HESS is a list keyword that specifies the Cartesian Hessian matrices. It is required in all
the REACT1, REACT2, PROD1, PROD2, WELLR, WELLP, and SADDLE sections (if they exists
and they are not atomic species). It is not required in all the POINT sections, but there
must be at least one POINT section with Hessian information on each side of the reaction
path.
Polyrate 260
SMEP
SMEP is a variable keyword that specifies the value of the reaction coordinate s at the
current grid point, in mass-scaled atomic units. This keyword is required and only
accepted in the POINT sections; for reactants, products, and wells the value of s is
calculated as described in Ref. 48 in Sect. 21. If the KIES keyword is on, the values in
SMEP are only used for ordering the points, but they could take any value that allow the
program to sort the points in its right order.
VMEP
VMEP is a variable keyword that specifies the value of VMEP(s) at the current grid point,
in atomic units and setting the zero of energy at reactants. This keyword is required and
only accepted in the POINT sections.
Polyrate 261
12.E. General description of file fu40 input
This file is needed only if the POTENTIAL keyword of the ENERGETICS section of file fu5 is
equal to unit40. The input from FORTRAN unit fu40 is in free format keyword style.
All input sections must start with the section name preceded by an “*”.
12.E.1 Section Descriptions
Section Name Description
*GEN40 general data such as options for input and extrapolation
*EXTRAP40 extrapolation information for the reactants and products
*R140 information for the first reactant
*R240 information for the second reactant
*P140 information for the first product
*P240 information for the second product
*WR40 information for reactant side well
*WP40 information for product side well
*SADDLE40 information for the saddle point
*POINT40 information for a point along the MEP
The POINT40 section should be repeated once for each of the points along the MEP excluding
the reactant limit, product limit, points used for extrapolation, and saddle point; i.e., POINT40
should be repeated once for each of the points s1,s2,s3,...sN (in the notation of pages 96-99
of Ref. 14 of Sect. 21) except the saddle point, and if there is a saddle point, that point should
not be specified in a POINT40 section. Each section appears at most once except POINT40,
which appears NPTS times. The sections can be in any order except that the POINT40 sections
must be in order of increasing s. The saddle point, if any, is specified in the SADDLE40
section. In reading in gradients and Hessians, the coordinates are always in this order: x, y, z
of atom 1, x, y, z of atom 2, etc.
Polyrate 262
12.E.2 GEN40 section
Keyword Type Default Description
TITLE list blank job title or comment
PRINT variable noextra print options
MAXLPTS variable 3 maximum number of points used in Lagrange interpolation
GEOMUNIT variable bohr unit for coordinate input
GRADUNIT variable bohr unit for gradient input
FREQSOURCE variable read option for obtaining frequencies
FREQUNIT variable waven option for frequency input
HESSFORM variable full form of Hessian matrix
HESSUNIT variable bohr option for Hessian matrix input
ANHARM variable none option for anharmonicity input
CURVATURE variable setzero curvature calculation options
GRADDER variable noextra option for computing the derivative of the gradient
NPTS variable 2 number of points along the MEP at which data is to be read
Polyrate 263
Glossary of GEN40 keywords
ANHARM
ANHARM is a variable keyword for selecting anharmonicity input.
Option Definition
none No anharmonic data is read (default).
cubic Read the third derivatives k3 with respect to the normal
coordinates at each grid point.
quartic Also read in fourth derivatives k4 with respect to the
normal
coordinates at each grid point.
Example: ANHARM cubic
CURVATURE
CURVATURE is a variable keyword used to select the way in which information about the curvature components BmF is input. For the compute option to be used,
freqsource must be set to hessian (and the Hessians must be provided in
SADDLE40 and POINT40).
Option Definition
setzero The BmF are set to zero everywhere (default).
read The BmF are read directly.
compute The BmF are computed from the gradient and Hessian as
discussed in Sections 6.H and 10.F.
Example: CURVATURE read
FREQSOURCE
FREQSOURCE is a variable keyword for selecting how the frequencies should be
determined.
Option Definition
read Frequencies are read directly (default).
hessian Frequencies are obtained by diagonalizing the Hessian or
projected Hessian matrix.
Example: FREQSOURCE hessian
Polyrate 264
FREQUNIT
FREQUNIT is a variable keyword that specifies the units of the input frequencies.
Option Definition
waven Frequencies are given in cm-1 (default)
au Frequencies are given in atomic units.
Example: FREQUNIT au
Note: all frequencies must be input in the same units (all wavenumbers or all atomic
units), including the imaginary frequency, WSTAR.
GEOMUNIT
GEOMUNIT is a variable keyword that specifies the units of the Cartesian or mass-scaled
Cartesian coordinates. If one of the mass-scaled options is chosen, then the scaling mass
µ must be specified in unit fu5 by the variable SCALEMASS in section PATH. If µ = 1 amu
is used for scaling, then SCALEMASS does not need to be specified since 1 amu is the
default.
Option Definition
coordinates are in:
bohr unscaled bohrs (default)
msbohr mass-scaled bohrs
ang unscaled angstroms
msang mass-scaled angstroms
si unscaled meters
Example: GEOMUNIT ang
GRADDER
GRADDER is a variable keyword used to select how the derivative of the gradient is
obtained for use in calculation of the curvature components BmF. This keyword is
utilized only if CURVATURE is set to compute.
Option Definition
noextra Derivative of the gradient with respect to s is obtained from a
quadratic fit of the gradient at three points on the basic input
grid, with the middle point being the current point on the
Hessian grid (default). In the notation of Section 9.C,
noextra means that the gradient grid is the basic input grid.
Polyrate 265
oneextra Derivative of the gradient is computed by one-sided finite
difference using the gradient on the basic input grid and a
gradient input at one extra point near the basic input grid point. oneextra means that the gradient grid has twice
as many points as the basic input grid.
twoextra Derivative of the gradient is computed from a quadratic fit
obtained using the gradient on the basic input grid and
gradients input at an extra point near and on each side of the
basic input grid point.
Example: GRADDER oneextra
GRADUNIT
GRADUNIT is a variable keyword that specifies the units of the gradients (or, if forces are
used, the unit of the force).
Option Definition
gradients are in: bohr hartrees per unscaled bohr (default)
msbohr hartrees per mass-scaled bohr
ang hartrees per unscaled Å
msang hartrees per mass-scaled Å
si joules per unscaled meter
Example: GRADUNIT msbohr
HESSFORM
HESSFORM is a variable keyword that, if hessian is specified in FREQSOURCE, specifies
the form of the Hessian matrix.
Option Definition
full F is input as the full matrix (default).
packed F is input in packed form.
Example: HESSFORM packed
If packed is selected, the lower triangular elements of F should be listed in order such
that F P i i jij = - +( ( ) )12
1 , where P(k) is element k of the input list and Fij is the
element of F in row i and column j. The number of elements listed per line is arbitrary.
Examples of both input forms for a 6 x 6 matrix is shown below:
Full matrix - example 1
Polyrate 266
F11 F12 F13 F14 F15 F16
F21 F22 F23 F24 F25 F26
F31 F32 F33 F34 F35 F36
F41 F42 F43 F44 F45 F46
F51 F52 F53 F54 F55 F56
F61 F62 F63 F64 F65 F66
Full matrix - example 2
F11 F12 F13 F14 F15 F16 F21 F22 F23
F24 F25 F26 F31 F32 F33 F34 F35 F36
F41 F42 F43 F44 F45 F46 F51 F52 F53
F54 F55 F56 F61 F62 F63 F64 F65 F66
Packed matrix - example 1
F11
F21 F22
F31 F32 F33
F41 F42 F43 F44
F51 F52 F53 F54 F55
F61 F62 F63 F64 F65 F66
Packed matrix - example 2
F11 F21 F22 F31 F32 F33
F41 F42 F43 F44 F51 F52
F53 F54 F55 F61 F62 F63
F64 F65 F66
The order of the coordinates is explained in Section 12.E.1.
Note that GAUSSIAN94 writes the packed Hessian matrix in a slightly different way in the
standard output file, but the Hessian in the formatted checkpoint file (requested by their
FormCheck keyword) is in precisely the packed form accepted by Polyrate and so is
convenient for copying and pasting into Polyrate fu40 files.
Note that the exact F matrix is symmetric, but due to finite precision in computations, the
actual matrix one has to input is usually nonsymmetric. If one inputs a nonsymmetric full
matrix, the code uses the unsymmetric matrix. If a user wants the code to use a
symmetric matrix, we recommend taking an arithmetic average of Fij and Fji for the
resulting symmetrized elements in packed form.
Polyrate 267
HESSUNIT
HESSUNIT is a variable keyword that, if hessian is specified in FREQSOURCE, specifies
the units of the Hessian matrix F. The choice of coordinates (mass-scaled or not) must be
consistent with GEOMUNIT.
Option Definition
Hessians are in:
bohr hartrees per unscaled bohr2 (default)
msbohr hartrees per mass-scaled bohr2
ang hartrees per unscaled Å2
msang hartrees per mass-scaled Å2
si joules per unscaled meter2
Example: HESSUNIT msbohr
Users calculating Hessians by an electronic structure package should read the manual for
that package to see what units the Hessian is in. For example, GAUSSIAN94 prints the
Hessian in hartrees per unscaled bohr2.
MAXLPTS
MAXLPTS is a variable keyword with an integer argument that specifies the maximum
number of points used in Lagrange interpolation in the procedure of Subsection 9.C. The
default value for this keyword is 3. If this keyword is set to –1, the program will
perform an IVTST-M calculation using the information read from the fu40 input file.
When using file fu40, the user cannot select any options for the IVTST-M calculation; it
will be performed according to the default options, and the number of gradient and
Hessian points have to be the same and equal to NPTS (see below). Therefore, only
IVTST-M-NPTS/NPTS calculations are allowed. The curvature components will be
interpolated using a value of 3 for the exponent in the mapping function. For
unimolecular reactions or reactions with wells, a cubic polynomial fitting to V is done previous to its spline fitting, taking a step of 0.01 a0 along the lowest frequency mode for
performing this fitting. The only way to change any of these options or to use a different
number of gradient and Hessian points is by using the fu31 input file, which is
specifically designed for IVTST-M calculations.
NPTS
Polyrate 268
NPTS is a variable keyword with an integer argument that specifies the number of points
along the MEP (excluding the reactant limit, product limit, points used for extrapolation,
and saddle point) at which data is to be read. Unless only TST reaction rates are
calculated, file fu40 must contain a minimum of one point on each side of the saddle
point. Unless NEXTPT is on, these points must be arranged in order of increasing s. The
section POINT40 should occur NPTS times in the file 40 input. The default value for NPTS
is 2.
PRINT is a variable keyword for selecting print options.
Option Definition
noextra Print out titles and options (default).
summary Also print out summary.
input Also echo input as it is read.
intermediate Also print out intermediate information about fitting
exponential functions and print out interpolated results each
time RPHINT is called. debugging Also print out debugging information in exponential fitting.
Example: PRINT summary
TITLE
TITLE is a list keyword that allows the user to give a one-line title to the
electronic structure file.
Polyrate 269
12.E.3 R140, R240, P140, P240, WR40, and WP40 sections
The R140, R240, P140, P240, WR40, and WP40 sections all have the same set of keywords.
A separate section is needed for each reactant, each product, and each well.
Keyword Type Default Description
SVALUE variable dgr (or dgp) value of s (in a.u.) at the reactant (or
product)
VVALUE variable (required) potential (in a.u.) at reactant (or
product)
HESSIAN list (see Glossary) Hessian matrix for the reactant or
product species
IFREQ list 1 2 3 ... indices for reordering frequencies,
anharmonicities, and curvature
components
FREQ list (see Glossary) vibrational frequencies for the
reactant or product species
3RDDERIV list (see Glossary) third derivatives of V with respect
to motion along the normal
coordinates for the reactant or
product
4THDERIV list (see Glossary) fourth derivatives of V with respect
to motion along the normal
coordinates for the reactant or
product
Polyrate 270
Glossary of R140, R240, P140, P240, WR40, and WP40 keywords
3RDDERIV
3RDDERIV is a list keyword that is used to specify the third derivatives of V along the
normal coordinates at the reactant, product, or well. If ANHARM is set to cubic or
quartic in the GEN40 section, this keyword is required unless the reactant or product
under consideration is monatomic.
4THDERIV
4THDERIV is a list keyword that is used to specify the fourth derivatives of V along the
normal coordinates at the reactant, product, or well. If ANHARM is set to quartic in
the GEN40 section, this keyword is required unless the reactant or product under
consideration is monatomic.
FREQ
FREQ is a list keyword that is used to specify the frequencies for each normal mode at the
reactant, product, or well species. This keyword is required if FREQSOURCE is set to
read (the default value) in the GEN40 section and is not used otherwise. The units of
the frequencies are determined by the FREQUNIT keyword in the GEN40 section.
HESSIAN
HESSIAN is a list keyword that is used to specify the Hessian matrix at the reactant, product, or well species. This keyword is required if FREQSOURCE is set to hessian in
the GEN40 section and is not used otherwise. The form and units of the Hessian matrix
are determined by the HESSFORM and HESSUNIT keywords in the GEN40 section,
respectively.
IFREQ
IFREQ is a required list keyword that is used to specify indices for reordering frequencies,
anharmonicities, and curvature components in the interpolation table in order to make the
ordering consistent with that at the saddle point and/or along the MEP. The imaginary
frequency at the saddle point is not included in this ordering. Therefore, index 1
corresponds to the largest frequency at the saddle point, index 2 corresponds to the
second largest frequency, and so on.
Polyrate 271
SVALUE
SVALUE is a variable keyword that specifies the value of s at the reactant if the reaction is
unimolecular or at the well on the reactant side or the value of s at the product if there is
only one product or at the well on the product side. The argument of SVALUE can be
either a numerical value (in bohr), dgr (default guess for reactant or well), or dgp
(default guess for product or well). SVALUE for reactants has meaning only for a
unimolecular reaction, and SVALUE for products has meaning only for a unimolecular
rearrangement or an association reaction. SVALUE should be omitted for the reactants if
there are two or more reactants, and SVALUE should be omitted for the products if there
are two or more products. In the following definitions, sR is the value of s at the reactant
or well on the reactant side, and sP is the value of s at the product or well on the product
side.
Option Definition
(numerical value) value of sR (R140 or WR40 section) or
sP (P140 or WP40 section)
dgr sa
s s s=
-
- -
ìíî
max.
( )
2 0 0
1 2 1
dgp
VVALUE
VVALUE is a required variable keyword that specifies the value of the potential (in a.u.) at
the reactant or product.
îíì
-+=
- )(
0.2max
1
0
NNN sss
as
Polyrate 272
12.E.4 SADDLE40 section
The SADDLE40 section is used to provide information at the saddle point, if it exists. This
section should be omitted if there is no saddle point.
Keyword Type Default Description
VVALUE variable (required) potential at saddle point
IFREQ list 1 2 3 ... indices for reordering frequencies, anharmonicities, and curvature components
HESSIAN list (see Glossary) Hessian matrix for the saddle point
FREQ list (see Glossary) vibrational frequencies for the saddle point
3RDDERIV list (see Glossary) third derivatives of V with respect to motion along the normal coordinates for the saddle point
4THDERIV list (see Glossary) fourth derivatives of V with respect to motion along the normal coordinates for the saddle point
WSTAR list (see Glossary) absolute value of the imaginary frequency at the saddle point
Polyrate 273
Glossary of SADDLE40 keywords
3RDDERIV
3RDDERIV is a list keyword that is used to specify the third derivatives of V along the
bound normal coordinates at the saddle point. This keyword is required if ANHARM is set
to cubic or quartic in the GEN40 section.
4THDERIV
4THDERIV is a list keyword that is used to specify the fourth derivatives of V along the
bound normal coordinates at the saddle point. This keyword is required if ANHARM is set to quartic in the GEN40 section.
FREQ
FREQ is a list keyword that is used to specify the frequencies for each bound normal mode
at the saddle point. This keyword is required if FREQSOURCE is set to read (the default
value) in the GEN40 section and is not used otherwise. The units of the frequencies are
determined by the FREQUNIT keyword in the GEN40 section.
HESSIAN
HESSIAN is a list keyword that is used to specify the Hessian matrix at the saddle point.
This keyword is required if FREQSOURCE is set to hessian in the GEN40 section and is
not used otherwise. The form and units of the Hessian are determined by the HESSFORM
and HESSUNIT keywords in the GEN40 section, respectively.
IFREQ
IFREQ is a required list keyword that is used to specify indices for reordering frequencies,
anharmonicities, and curvature components in the interpolation table for the saddle point.
VVALUE
VVALUE is a required variable keyword that specifies the value of the potential (in a.u.) at
the saddle point.
WSTAR
WSTAR is a variable keyword that is used to specify the value of the imaginary frequency at the saddle point. This keyword is required if FREQSOURCE is set to read (the default
value) in the GEN40 section and is not used otherwise. The default unit for the imaginary
frequency is cm-1, but can be changed to atomic units by setting FREQUNIT to au.
Polyrate 274
12.E.5 POINT40 section
This section should be repeated for each point along the MEP except for the reactant
limit, product limit, points used for extrapolation, and saddle point. The points must be
arranged starting from the one with the most negative s value and continuing in the
direction of increasing s.
SMEP variable (required) value of s at the current grid location along the MEP
VMEP variable (required) potential at the current grid location on the MEP
GEOM list (required) Cartesian coordinates at the current grid point
GRADS list (required) gradient vector at s along MEP
FORCES list (required) force vector at s along MEP
SB1 variable (see Glossary) value of s at a location along the MEP near the current grid point
GRADSB1 list (see Glossary) gradient vector at the extra point SB1 for computing the curvature B
FORCESB1 list (see Glossary) force vector at the extra point SB1
for computing the curvature B
SB2 variable (see Glossary) value of s at another location along the MEP near the current grid point
GRADSB2 list (see Glossary) gradient vector at the extra point SB2 for computing the curvature B
FORCESB2 list (see Glossary) force vector at the extra point SB2 for computing the curvature B
IFREQ list 1 2 3 ... indices for reordering frequencies, anharmonicities, and curvature components
Keyword Type Default Description
Polyrate 275
HESSIAN list (see Glossary) Hessian matrix at the current grid point
FREQ list (see Glossary) vibrational frequencies at the current grid point
3RDDERIV list (see Glossary) third derivatives of V with respect to motion along the normal coordinates for the current grid point
4THDERIV list (see Glossary) fourth derivatives of V with respect to motion along the normal coordinates for the current grid point
BFS list (see Glossary) reaction path curvature components at the current grid point along the MEP
Keyword Type Default Description
Polyrate 276
Glossary of POINT40 keywords
3RDDERIV
3RDDERIV is a list keyword that is used to specify the third derivatives of V along the
bound normal coordinates at the current grid point. This keyword is required if ANHARM
is set to cubic or quartic in the GEN40 section.
4THDERIV
4THDERIV is a list keyword that is used to specify the fourth derivatives of V along the
bound normal coordinates at the current grid point. This keyword is required if ANHARM is set to quartic in the GEN40 section.
BFS
BFS is a list keyword that is used to specify the reaction path curvature components at the
current grid point along the MEP. This keyword is required if CURVATURE is set to read
in the GEN40 section and is not used otherwise.
FORCES
FORCES is a list keyword that is used to specify the forces at the current grid point. This
keyword is required if GRADS is not used. The units of the force are determined by the
GRADUNIT keyword in the GEN40 section.
FORCESB1
FORCESB1 is a list keyword that is used to specify the force at s = SB1. This keyword is
required if GRADDER is set to oneextra or twoextra in the GEN40 section and
GRADSB1 is not used; otherwise, it is not used.
FORCESB2
FORCESB2 is a list keyword that is used to specify the force at s = SB2. This keyword is required if GRADDER is set to twoextra in the GEN40 section and GRADSB2 is not used;
otherwise, it is not used.
FREQ
FREQ is a list keyword that is used to specify the frequencies for each bound generalized
normal mode at the current grid point. This keyword is required if FREQSOURCE is set to
read (the default value) in the GEN40 section and is not used otherwise. The units of
the frequencies are determined by the FREQUNIT keyword in the GEN40 section.
Polyrate 277
GEOM
GEOM is a list keyword that specifies the Cartesian coordinates at the current grid
location, in units determined by the GEOMUNIT keyword in the GEN40 section.
GRADS
GRADS is a list keyword that is used to specify the gradient at the current grid point. This
keyword is required if FORCES is not used. The units of the gradient are determined by
the GRADUNIT keyword in the GEN40 section.
GRADSB1
GRADSB1 is a list keyword that is used to specify the gradient at s = SB1. This keyword is
required if GRADDER is set to oneextra or twoextra in the GEN40 section and
FORCESB1 is not used; otherwise, it is not used.
GRADSB2
GRADSB2 is a list keyword that is used to specify the gradient at s = SB2. This keyword is required if GRADDER is set to twoextra in the GEN40 section and FORCESB2 is not
used; otherwise, it is not used.
HESSIAN
HESSIAN is a list keyword that is used to specify the Hessian matrix at the current grid
point. This keyword is required if FREQSOURCE is set to hessian in the GEN40 section
and is not used otherwise. The form and units of the Hessian are determined by the
HESSFORM and HESSUNIT keywords in the GEN40 section, respectively.
IFREQ
IFREQ is a list keyword that is used to specify indices for reordering frequencies,
anharmonicities, and curvature components in the interpolation table for the current grid
point.
SMEP
SMEP is a required variable keyword that specifies the value of s (in bohr) at the current
grid location along the MEP.
SB1
SB1 is a variable keyword that specifies the value of s (in bohr) at a grid location along
the MEP close to SMEP. This keyword is required if GRADDER is set to oneextra or
twoextra in the GEN40 section and is not used otherwise.
Polyrate 278
SB2
SB2 is a variable keyword that specifies the value of s (in bohr) at a grid location along
the MEP close to SMEP, but on the opposite side of SMEP from SB1. This keyword is
required if GRADDER is set to twoextra in the GEN40 section and is not used
otherwise.
VMEP
VMEP is a required variable keyword that specifies the value of the potential at the current
grid location.
Polyrate 279
12.F. General description of unit fu50 input
This file is only needed if the DL keyword is set to ioc in the GENERAL section of the unit
fu5 input. This allows one to calculate zero-order interpolated VTST or interpolated
optimized corrections. The input from FORTRAN unit fu50 is in free format keyword
style. In the current version of Polyrate there is only one section, VTSTIC, in the unit fu50
input file, and the first keyword in this file must be *VTSTIC. A sample unit fu50 input
file is cmcic.dat for the cmctr2 test run. A description of the input to the Polyrate code
from FORTRAN unit fu50 follows.
Keyword Type Default Description
0IVTST switch off zero-order IVTST calculation
(NO)DETMI list no correction
corrected det I
ENERXN variable required corrected exoergicity
ENESAD variable required corrected classical barrier height
(NO)FREQMAT list no matching frequency matching information
(NO)HRMI variable 99 correct the moment of inertia
FREQIMAG variable required imaginary freq. at saddle point
LOWFREQ list no correction
IVTST treatment of low freq.
MEPTYPER variable two type of reactant-side MEP
MEPTYPEP variable two type of product-side MEP
MIRP list not used corrected moments of inertia for the reactant and product
MITS list not used corrected moments of inertia for the transition state
LCTCOR variable no correction of V in the nonadiabatic region in LCT calculations
Polyrate 280
Keyword Type Default Description
PCFREQA list not used corrected frequencies of the product-side stationary point
PCFREQS list not used lower-level frequencies of the product-side stationary point
PCINFO list not used product-side stationary point info.
SPC variable not used s value at this point
ENEPCS variable not used lower-level V at this point
ENEPCA variable not used corrected V at this point
(NO)PRODFREQ list not used corrected product frequencies
RCFREQA list not used corrected frequencies of the reactant-side stationary point
RCFREQS list not used lower-level frequencies of the reactant-side stationary point
RCINFO list not used reactant-side stationary point info.
SRC variable not used s value at this point
ENERCS variable not used lower-level V at this point
ENERCA variable not used corrected V at this point
RANGEIC list not used range parameters
RPL variable 1.0 range parameter L for an Eckart function
BR variable 5.0 range parameter for a cut-off Gaussian on the reactant side
BP variable 5.0 range parameter for a cut-off Gaussian on the product side
REACFREQ list not used corrected reactant frequencies
SADFREQ list not used corrected saddle point frequencies
UNITMI variable au units used for det I input
Polyrate 281
Glossary for file fu50 keywords
0IVTST
0IVTST is a switch keyword that specifies that the zero-order IVTST calculation will be
performed. The default is off.
DETMI (NODETMI)
DETMI is a list keyword used to input the corrected determinant of the moment of inertia
tensor. Five values of det I (which is the determinant of the inertia tensor, also equal to
the product of the three principal moments of inertia) have to be input. They are, in the
order of input, for the first reactant species, the second reactant species, the saddle point,
the first product species, and the second product species. The units used are specified by
the UNITMI keyword, which is discussed latter in this section. For an atomic species, the
user should input a value of zero for det I. The default is NODETMI, i.e., no correction for
det I.
Example: DETMI
5.7220E16
4.9906E13
9.8871E17
5.9964E16
2.3769E13
END
ENERXN
ENERXN is a variable keyword used to input the corrected energy of the reaction in
kcal/mol, excluding zero point contributions. This is a required keyword. It should be
positive if the reaction is endoergic and negative if it is exoergic.
Example: ENERXN -5.0
ENESAD
ENESAD is a variable keyword used to input the corrected classical barrier height in
kcal/mol. This is a required keyword.
Example: ENESAD 6.0
Polyrate 282
FREQMAT (NOFREQMAT)
FREQMAT is a list keyword used to specify the frequency matching information. The
input consists of n lines where n is the number of real saddle point frequencies. Each line
needs three numbers; the first one is the mode number of a mode at the saddle point, and
the second and the third ones are the mode numbers of the modes at the reactant-side and
product-side stationary points which match that saddle point mode. The default is
NOFREQMAT, i.e., the vibrational frequencies are automatically matched in decreasing
order. However, if the keywords MEPTYPER and MEPTYPEP, which are discussed latter in
this section, are not both equal to two, this keyword is required.
Example: FREQMAT
1 2 1
2 3 3
3 4 2
4 1 4
5 5 5
6 6 6
7 8 7
8 7 8
9 9 9
END
HRMI (NOHRMI)
HRMI is a variable keyword that specifies the correction method for the moment of inertia
of hindered-rotor modes. The default is NOHRMI. The valid arguments for the HRMI
keyword are:
Option Description
all correct the moments of inertia of all the hindered-rotor modes of
the reactants, products, and saddle point. -n(n=1,2...) same as above, and set the moments of inertia of the lowest n
GTS hindered-rotor modes for all values of s to their values at
the saddle point.
n(n=1,2...) no correction to the moment of inertia at stationary points, but set
the moments of inertia of the lowest n GTS hindered-rotor modes
for all values of s to their lower-level values at the saddle point.
Example: HRMI -1
Polyrate 283
FREQIMAG
FREQIMAG is a variable keyword used to input the absolute value of the corrected
imaginary frequency at saddle point in cm−1. This is a required keyword.
Example: FREQIMAG 900.0
LCTCOR
LCTCOR is a variable keyword that specifies the method to correct the potential energy in
the nonadiabatic region in LCT calculations. This keyword has an effect only when LCT
calculations are performed. The default is quadlin, which provides the standard
version of the VTST-IC method as explained in Section 3.1 of Ref. 36 of Sect. 21. The
valid arguments for this keyword are:
Option Description
quadlin linear or quadratic correction depending on the magnitude of the
corrections in different regions linear linear correction only
nocor no correction
Example: LCTCOR nocor
Note: The user should take special care to make sure that this correction yields
physical results.
LOWFREQ
LOWFREQ is a list keyword used to specify that certain GTS mode frequencies are to be
interpolated using the IVTST-0 formula based on their values at three points. The
functional forms used to interpolate the specified frequencies are the same as the
IVTST-0 functions as explained in Section 4.1 of Ref. 36 of Sect. 21. Notice that this is
similar to the IVTST0FREQ keyword of the PATH section of fu5. IVTST0FREQ is used for
single-level calculations and lower levels of dual-level calculations, whereas LOWFREQ is
used for the higher level of dual-level runs. If, for a given mode, IVTST0FREQ and
LOWFREQ are both specified, then LOWFREQ overrides IVTST0FREQ.
Example: LOWFREQ
11
12
13
14
END
Polyrate 284
MEPTYPER
MEPTYPER is a variable keyword that specifies the type of reactant-side MEP that will be
considered in the VTST-IOC calculation. The default value is two. The valid arguments
for this keyword are:
Option Description one There is only one reactant species and interpolation is carried out
between this species and the saddle point.
two There are two reactant species and interpolation is carried out
between these species (using the merged set of frequencies) and
the saddle point.
well The correction on the reactant side is based on a well.
Example: MEPTYPER one
MEPTYPEP
MEPTYPEP is a variable keyword that specifies the type of product-side MEP that will be
considered in the VTST-IOC calculation. The default is two. The valid arguments for
this keyword are:
Option Description
one There is only one product species and interpolation is carried out
between this species and the saddle point. two There are two product species and interpolation is carried out
between these species (using the merged set of frequencies) and
the saddle point.
well The correction on the product side is based on a well.
Example: MEPTYPER well
Polyrate 285
MIRP
MIRP is a list keyword used to input the corrected moments of inertia in atomic units of
the reactant and product hindered-rotor modes. This moment of inertial is for the internal
rotation, which is not the same as the moment of inertia of the overall system. This
keyword is needed if HRMI is set to all or is less than zero. The input order is reactant
1, reactant 2 (if any), product 1, and product 2 (if any); and within each reactant and
product species the modes should be ordered from the highest frequency hindered-rotor
mode to the lowest frequency hindered-rotor mode. This keyword can be omitted if there
are no hindered-rotor modes in reactants and products.
Example: MIRP
960.50
END
MITS
MITS is a list keyword used to input the corrected moments of inertia in atomic units of
the saddle point hindered-rotor modes. The moment of inertia is for the internal rotation,
and it is not the same as the moment of inertial of the overall system. This keyword is needed if HRMI is set to all or is less than zero. The input should be ordered from the
highest frequency hindered-rotor mode to the lowest frequency hindered-rotor mode.
This keyword can be omitted if there are no hindered-rotor modes at the saddle point. In
the example below, which is for the CH4 + OH reaction, the symmetry number for the
internal rotation of the CH3 group around the C−H axis in the TS is 3:
Example: MITS
7690
Polyrate 286
END
PCFREQA
PCFREQA is a list keyword used to input the corrected frequencies (in cm−1) of the
product-side stationary point used for the IOC correction. If the number of real frequencies is less than that of the saddle point (i.e., when MEPTYPEP is two), add zeros
after the last non-zero frequency to input a total of n frequencies, where n is the number
of real frequencies at the saddle point. There should be n + 1 input frequencies if
MEPTYPEP is not two. The order of the frequencies in the input must match the order of
the lower-level frequencies, i.e., the first frequency must correspond physically to the
highest lower-level frequency, and the second frequency must correspond physically to
the second highest lower-level frequency, and so on.
Example: PCFREQA
3124.0 2282.0 2282.0 2279.0 1489.0
1489.0 1287.0 1287.0 1111.0 1072.0
1033.0 1033.0 565.0 415.0 411.0
0.0 0.0 0.0 0.0 0.0
END
(In this example MEPTYPEP is two and there are nine atoms in the system. The first
product has four atoms and the second product has five atoms. The saddle point has
twenty real frequencies but the products have only fifteen real frequencies, so we add five
zeros at the end of input.)
PCFREQS
PCFREQS is a list keyword used to input the lower-level frequencies (in cm−1) of the product-side stationary point. This keyword is only needed when MEPTYPEP is well.
Otherwise the frequencies are just the product frequencies, and the program will have this
information when it calculates the product properties. There should be n+1 input
frequencies, where n is the number of the real frequencies at the saddle point. The
frequencies in the input must be in decreasing order.
Example: PCFREQS
3124.0 2282.0 2282.0 2279.0 1489.0
1489.0 1287.0 1287.0 1111.0 1072.0
1033.0 1033.0 565.0 415.0 411.0
END
Polyrate 287
PCINFO
PCINFO is a list keyword used to specify the product-side stationary point information.
This keyword is needed only if MEPTYPEP is one or well. The valid subkeyword
options are defined below. There are no defaults for these subkeywords, and the user
must supply all the values, except as noted.
Option Description spc s value in bohrs at this point
enepcs lower-level potential energy in kcal/mol at this point
(required only if MEPTYPEP is well)
enepca corrected potential energy in kcal/mol at this point (required
only if MEPTYPEP is well)
nofreqcorr no frequency correction at the product complex; when this
keyword is used the keywords PCFREQA and PCFREQS are not
needed
Example: PCINFO
SPC 3.0
ENEPCS -10.0
ENEPCA -9.0
END
PRODFREQ (NOPRODFREQ)
PRODFREQ is a list keyword used to input the corrected product frequencies in cm−1. It is
only needed when MEPTYPEP is well; otherwise the corrected product frequencies are
input in the PCFREQA keyword. NOPRODFREQ specifies that no correction is needed for the product frequencies, but this is allowed only if MEPTYPEP is well. The default is to
correct the product frequencies when MEPTYPEP is well, so if NOPRODFREQ is not
specified, the PRODFREQ keyword is required. See keyword PCFREQA for the required
input order for the frequencies.
Example: PRODFREQ
3092.0 3092.0 2981.0 1453.0 1453.0
1377.0 1017.0 1017.0 741.0
END
Polyrate 288
RCFREQA
RCFREQA is a list keyword used to input the corrected frequencies (in cm−1) of the
reactant-side stationary point that the IOC correction is based on. If the number of real
frequencies is less than that of the saddle point (i.e., when MEPTYPER is two), add zeros
after the last non-zero frequency to input a total of n frequencies, where n is the number
of real frequencies at the saddle point. There should be n+1 input frequencies if MEPTYPER is not two. The order of the frequencies in the input must match the order of
the lower-level frequencies, i.e., the first frequency must correspond physically to the
highest lower-level frequency, and the second frequency must correspond physically to
the second highest lower-level frequency, and so on.
Example (see the example for the PCFREQA keyword): RCFREQA
3124.0 2282.0 2282.0 2279.0 1489.0
1489.0 1287.0 1287.0 1111.0 1072.0
1033.0 1033.0 565.0 415.0 411.0
0.0 0.0 0.0 0.0 0.0
END
RCFREQS
RCFREQS is a list keyword used to input the flower-level frequencies (in cm−1) of the
reactant-side stationary point. This keyword is only needed when MEPTYPER is well.
Otherwise the frequencies are just the reactant frequencies, and the program will have
this information when it calculates the reactant properties. There should be n + 1 input
frequencies, where n is the number of the real frequencies at the saddle point. The
frequencies in the input must be in decreasing order.
Example: RCFREQS 3124.0 2282.0 2282.0 2279.0 1489.0
1489.0 1287.0 1287.0 1111.0 1072.0
1033.0 1033.0 565.0 415.0 411.0
END
Polyrate 289
RCINFO
RCINFO is a list keyword used to specify the reactant-side stationary point information.
This keyword is needed only if MEPTYPER is one or well. The valid subkeyword
options are defined below. There are no defaults for these subkeywords, and the user
must supply all the values, except as noted.
Option Description src s value in bohrs at this point
enercs lower-level potential energy in kcal/mol at this point
(required only if MEPTYPER is well)
enerca corrected potential energy in kcal/mol at this point (required
only if MEPTYPER is well)
nofreqcorr no frequency correction at the reactant complex; when this
keyword is used the keywords RCFREQA and RCFREQS are not
needed
Example: RCINFO
SRC -3.0
ENERCS -5.0
ENERCA -4.0
END
RANGEIC
RANGEIC is a list keyword used to input the range parameters for the correction functions
in the VTST-IOC calculations. The valid subkeyword options are defined below.
Option Description Default
rpl range parameter L in bohrs for an Eckart function 1.0
br range parameter for a cut-off Gaussian function on 5.0
the reactant side
bp range parameter for a cut-off Gaussian function on 5.0
the product side
Example: RANGEIC
RPL 0.3
BR 10.0
BP 8.0
END
Polyrate 290
REACFREQ
REACFREQ is a list keyword used to input the corrected reactant frequencies in cm−1. It is
required if MEPTYPER is well. Otherwise the reactant frequencies are input in RCFREQA
keyword. See keyword RCFREQA for the requirement on the input order of the
frequencies.
Example: REACFREQ
3092.0 3092.0 2981.0 1453.0 1453.0
1377.0 1017.0 1017.0 741.0
END
SADFREQ
SADFREQ is a list keyword used to input the corrected real saddle point frequencies in
cm−1. It is a required keyword. See keyword RCFREQA for the required input order for
the frequencies.
Example: SADFREQ
3748.0 3130.0 3259.0 3255.0 1414.0
1521.0 1494.0 1298.0 1206.0 933.0
769.0 357.0 316.0 40.0
END
UNITMI
UNITMI is a variable keyword that specifies the units used for the DETMI keyword input. The default is au. The valid arguments are:
Option Description
au atomic units
si SI units, i.e., kg m2 or (kg m2)3
cgs c.g.s. units, i.e., g cm2 or (g cm2)3
scale scaled units, i.e., 10−40 g cm2 or (10−40 g cm2)3
amu atomic mass unit, i.e., a.m.u. bohr2 or (a.m.u. bohr2)3 .
Example: UNITMI AMU
Polyrate 291
12.G. General description of unit fu51 input
This file is only needed if the ispe option is specified with the DL keyword in the
GENERAL section of unit fu5. The single-point energy correction (VTST-ISPE) is used to
correct the energies along the reaction path. The input from FORTRAN unit fu51 is in
free format keyword style. A description of the input to the Polyrate code from
FORTRAN unit fu51 follows.
12.G.1. Section Descriptions
Section Name Description
*ISPEGEN general section for stationary point information
*POINT section for the extra points along the reaction path
The *POINT section should be repeated once for each of the points along the reaction path
excluding the reactants, products, saddle point, and wells.
Polyrate 292
12.G.2 ISPEGEN section
The *ISPEGEN section is used to provide information at the stationary points.
Keyword Type Default Description
EXERXN variable required corrected exoergicity
ENESAD variable required corrected classical barrier height
MEPTYPER variable two type of reactant-side MEP
MEPTYPEP variable two type of product-side MEP
PCINFO list not used product-side stationary point data
SPC variable not used value of s at this point
ENEPCS variable not used lower-level V at this point
ENEPCA variable not used corrected V at this point
RCINFO list not used reactant-side stationary point data
SRC variable not used value of s at this point
ENERCS variable not used lower-level V at this point
ENERCA variable not used corrected V at this point
Polyrate 293
Glossary of ISPEGEN keywords
EXERXN
EXERXN is a variable keyword used to input the corrected classical energy change of the
reaction in kcal/mol, excluding zero-point contributions. This is a required keyword. It
should be positive if the reaction is endoergic and negative if it is exoergic. In other
words, this is the corrected product energy relative to the reactant energy.
Example: EXERXN -5.0
ENESAD
ENESAD is a variable keyword used to input the corrected classical barrier height in
kcal/mol. This is a required keyword.
Example: ENESAD 6.0
MEPTYPEP
MEPTYPEP is a variable keyword that specifies the type of product-side MEP that will be
considered in the VTST-ISPE calculation. The default is two. The valid arguments for
this keyword are:
Option Description
one There is one product and wells, if any, are not
recognized. two There are two products and wells, if any, are not
recognized.
well A product well is recognized.
Example: MEPTYPEP one
MEPTYPER
MEPTYPER is a variable keyword that specifies the type of reactant-side MEP that will be considered in the VTST-ISPE calculation. The default is two. The valid arguments for
this keyword are:
Option Description
one There is one reactant and wells, if any, are not recognized.
Polyrate 294
two There are two reactants and wells, if any, are not
recognized. well A reactant well is recognized.
Example: MEPTYPER one
PCINFO
PCINFO is a list keyword used to specify the product-side stationary point information.
This keyword is needed only if MEPTYPEP is set to one or well. There are no defaults
for these options, the user must supply all values except as otherwise noted. The valid
options for this keyword are:
Option Description spc value of s, in bohrs, at this point
enepcs lower-level potential energy, in kcal/mol, at this point with
respect to the reactant (required if and only if MEPTYPEP is
set to well)
enepca corrected potential energy, in kcal/mol, at this point with
respect to the reactant (required if and only if MEPTYPEP is
set to well)
Example:
PCINFO spc 3.0
enepcs -10.0
enepca -9.0
RCINFO
RCINFO is a list keyword used to specify the reactant-side stationary point information.
This keyword is needed only if MEPTYPER is set to one or well. There are no defaults
for these options, the user must supply all values except as otherwise noted. The val id
options for this keyword are:
Option Description src value of s, in bohrs, at this point
enercs lower-level potential energy, in kcal/mol, at this point with
respect to the reactant (required if and only if MEPTYPER is
set to well)
enerca corrected potential energy, in kcal/mol, at this point with
respect to the reactant (required if and only if MEPTYPER is
set to well)
Polyrate 295
Example:
PCINFO src -3.0
enercs -5.0
enerca -4.0
Polyrate 296
12.G.3 POINT section
The POINT section should be repeated for each point along the MEP, except for the
reactants, products, saddle point, and wells. Each new POINT section must begin with
*POINT. The points can be arranged in any order.
Keyword Type Default Description
DVMEP variable variable difference in the corrected energy at point
SMEP variable required value of s at point
VMEP variable variable corrected energy at point
Notice that in the POINT section, the keyword SMEP is required and either VMEP or
DVMEP is needed for indicating the energy at a higher-level or difference of the energy at
a higher-level to the lower-level one.
Glossary of POINT keywords
DVMEP
DVMEP is a variable keyword that can be used to specify the energy difference between
the higher-level along the MEP from the lower-level ones. Using the VMEP keyword to
indicate the higher-level potential energies along the lower-level MEP has a limitation,
namely that the point chosen has to be a save-grid point of the lower-level path.
However, using the DVMEP keyword, the point chosen does not have to be a save-grid
point of the lower-level path because the difference in potential energies from the higher-
level to the lower-level is read instead of calculated.
Example: VMEP 5.1608
SMEP
SMEP is a variable keyword that specifies the value of s, in bohrs, at the current point
along the MEP.
Example: SMEP -0.8
Polyrate 297
VMEP
VMEP is a variable keyword that specifies the energy at the current point along the MEP.
Example: VMEP 10.5
Polyrate 298
13. DESCRIPTION OF INPUT FOR VRC-VTST
In VRC-VTST rate calculations, input file fu5 is the only one required; the other input
files used in RP-VTST calculations are not needed.
13.A Section descriptions of input file fu5
The following input sections correspond to the major parts of a VRC-VTST rate
calculation. Each section begins with a line giving the section name, preceded by an “*”.
Keywords for each section are discussed further in the rest of this subsection. In each
section, we list the keywords used in VRC-VTST rate calculations. The keywords that
are only used for VRC-VTST are discussed in this section; the keywords that can be used
for both RP-VTST and VRC-VTST are not discussed again and users can find the details
in Section 12.
Section Name Description
*GENERAL general data such as the title and defining the atoms involved
*ENERGETICS options for computing potential energy
*REACT1 definition and properties of the first reactant
*REACT2 definition and properties of the second reactant
*START Only used to define the electronic degeneracy for generalized
transition state
*PROD1 definition and properties of the first product
*PATH definition of reaction coordinate range and step size
*RATE options for computing the reaction rate
13.A.1. GENERAL section
The table below lists all the valid keywords for the GENERAL section. Indented keywords
are level-2 keywords, and the others are level-1 keywords. Level-2 keywords are always
Polyrate 299
associated with a level-1 list keyword and must come after that keyword and before any
other level-1 keyword or starred header. In the alphabetical glossary that follows the box
that are only used for VRC-VTST rate calculations. In any run for VRC-VTST this
section would have the TITLE, ATOMS, and VRC keywords.
Basic:
Keyword Type Default Description
TITLE list blank title with 5 lines maximum
ATOMS list required atoms in system
CHECK switch off check the input data
INPUNIT variable angstrom specifies the units in fu5 input file
OUTUNIT variable angstrom specifies the units in fu6 and fu14 output files
SUPERMOL switch on supermolecule mode for reactants and products
VRC switch Off use variable reaction coordinate to treat association reaction with loose transition state
VRCOPT list not used variable reaction coordinate algorithm options
JMAX variable 300 maximum angular momentum quantum number J in E,J -VT
JSTEP variable 5 step size in the integral over J in E,J -VT
GTYPE variable 4 type of random number generator in SPRNG
NITER variable 4 Gauss-Laguerre quadrature
NMC variable 1000 number of Monte Carlo samples per facet in multifaceted dividing surface
Polyrate 300
Glossary of GENERAL keywords only used for VRC-VTST
VRC
VRC is a switch keyword that allows the user to employ the variable reaction coordinate
algorithm to treat loose transition states. When this keyword is turned on, the PROD1,
PROD2, WELLR, WELLP, and START sections are not used in fu5 input file. Only forward
reaction rates will be calculated in this case. If each reactant has only one pivot point, a
spherical (i.e. single-faceted) dividing surface will be used. If more than one pivot point
is assigned to one or two of the reactants, a multifaceted dividing surface will be used.
Any keywords related the MEP algorithm are not used when VRC is turned on.
VRCOPT
VRCOPT is a list keyword that allows the user control over the parameters used in
variable reaction coordinate algorithm. If VRCOPT is given then it is assumed that the VRC
calculation is desired and the default for VRC becomes on. The valid options are defined
below.
Polyrate 301
Option Description Default
jmax maximum angular momentum quantum number J 300
calculated for the number of accessible state N(E,J ) in
E,J -VT
jstep step size of angular momentum quantum number J in the 5
integral over J to calculate the contribution to reactive
flux from transitional modes
gtype the type of random number generator in SPRNG package. 4
Type 4 is Multiplicative Lagged Fibonacci Generator in
SPRNG version 2.0. It is not recommended to change the
default value. User needs to refer SPRNG manual to
change the value to the desired type. niter number of Gauss-Laguerre quadrature points for total 4
energy E.
nmc number of Monte Carlo sampling for each facet in a 1000
multifaceted dividing surface. In parallel calculation, the
actual number used in the calculation may be changed
according to the number of processors used. If the
remainder when NMC is divided by number of processors
is not zero or NMC is smaller than number of processors,
the number of sampling for each processor will be
int(NMC/number of processors) + 1. User need to be
careful to balance the nmc and number of processors
used in parallel calculation.
Example: VRCOPT
NMC 600
JMAX 500
JSTEP 10
END
Polyrate 302
13.A.2. ENERGETICS section
The ENERGETICS section is used to define the method for computing the potential energy
of the reacting system. The table below lists all the valid keywords for the ENERGETICS
section. In the alphabetical glossary a more complete explanation for each keyword is
given.
Keyword Type Default Description
EZERO variable calculate method for determining zero of E
EZUNIT variable a.u. units of zero of energy
POTENTIAL variable hooks type of PES to be used
Glossary of ENERGETICS keywords
EZERO
Refer to Section 12.A.3
EZUNIT
Refer to Section 12.A.3
POTENTIAL
POTENTIAL is a variable keyword that allows the user to specify the source of the potential
energy information for a single-level calculation. There are only one valid option for a
VRC-VTST calculation, namely hooks. The option hooks means that the user is
providing potential information through the hooks. When Polyrate is used as a stand-
alone package, the hooks call SURF and SETUP; this is how one supplies an analytic
potential energy surface. When Polyrate is used in conjunction with a interface program,
e.g. GAUSSRATE, the hooks call the corresponding electronic structure program to
perform electronic structure calculations to obtained potential energy.
Option Definition
hooks use the hooks
Example: POTENTIAL hooks
Polyrate 303
13.A.3. OPTIMIZATION section
The OPTIMIZATION section is used to specify the method for carrying out geometry
optimizations when the POTENTIAL keyword selection is hooks. In principle, the
keywords used for RP-VTST can also be used for VRC-VTST to optimize reactants. But
these keywords have not been tested for VRC-VTST calculations. Therefore it is strongly
recommended to input the optimized geometries instead of using Polyrate to optimize the
reactant geometries because a semi-global analytical potential energy surface when using
Polyrate as a stand-alone package is required in VRC-VTST calculation and it usually
doesn’t have analytical derivatives used for geometry optimization.
Polyrate 304
13.A.4. REACT1, REACT2, PROD1, AND START sections
The summary table below gives the keywords that can be used for a VRC-VTST
calculations in REACT1, REACT2, PROD1, and START sections. Note that in VRC-VTST
calculations an additional keyword is introduced for setting the Cartesian coordinates of
pivot points used for the variable reaction coordinate. These pivot points are only
required in the REACT1 and REACT2 sections.
In START section, only the ELEC keyword is used. This gives electronic degeneracy of
the generalized transition state. No other keyword is required in this section when
Polyrate runs as a stand-alone program. When running in direct dynamics with other rate
program, e.g. GAUSSRATE, the STATUS keyword should be set to 6 to avoid any electronic
structure calculation for START section.
Polyrate 305
Basic:
Keyword Type Default Description
Required:
GEOM list required Cartesian coordinates of atoms
PIVOT list Required only
for reactants
Cartesian coordinates of pivot
points for reactants
Common:
ELEC list
all degen. = 1 electronic degeneracies
ENERGY variable none energy of the stationary point
FREQ switch on perform normal-mode analysis
FREQUNIT variable waven units of the frequencies
INITGEO variable geom location of input data that specify initial geometries
STATUS variable 0 status of the stationary point work
SPECIES variable nonlinrp species type (linearity)
VIB list none
frequencies of the stationary
points
Polyrate 306
Glossary of REACT1 and REACT2 keywords
PIVOT
PIVOT is a list keyword that is used to define the locations of pivot points. The Cartesian
coordinates of pivot points must be given along with their identification number. The
identification number can be the same for pivot points on the different reactants. The
origin of the Cartesian coordinates must be the same as the origin of the corresponding
reactant Cartesian coordinates, so that they can give the positions relative to the
corresponding reactant.
Example: PIVOT
1 0.000000 0.000000 0.200000
2 0.000000 0.000000 -0.200000
END
Polyrate 307
13.A.5. PATH section
The PATH section contains the keywords that control the calculation of the reaction path.
In VRC-VTST rate calculations, only one keyword, SVRC, is allowed in this section.
SVRC
SVRC is a list keyword that specifies the reaction coordinate s range and step size used in
variable reaction coordinate and single-faceted or multifaceted dividing surface algorithm
for loose transition state. If VRC keyword in GENERAL section is turned on, user needs to
specify this keyword only in the PATH section, and the other keywords in the PATH
section are not required.
Example: SVRC
2.0 4.0 0.1
END
This example tells the program that the s range is 2.0 – 4.0 Å (note that default unit is Å)
and that the step size is 0.1 Å.
Polyrate 308
13.A.6. RATE section
The RATE section contains the keywords that control the rate constant calculations. Note
that a conventional TST calculation is not a valid option for VRC-VTST rate since there is
no barrier on potential energy surface. Only forward rate constants (bimolecular
association rate) are calculated for VRC-VTS and the reverse unimolecular dissociation
rate calculation is not implemented yet. The VRC-VTST rate constants are calculated by
CVT, VT, and E,J -VT. An alphabetical glossary of all the keywords follows the
summary table.
Keyword Type Default Description
SIGMAF variable 1.0 sym. factor for forward reaction
SIGMAR Variable 1.0 sym. Factor for reversed reaction
TEMP list see below temperatures for rate calculations
SIGMAF
SIGMAF is a variable keyword whose argument specifies the number of equivalent ways
for forming the GTS for the forward reaction. Note that only two values are used in
VRC-VTST calculations. The value should be 1 for the case where the two reactants are
different, and the value should be 0.5 for the case two reactants are identical.
SIGMAR
SIGMAF is a variable keyword whose argument specifies the number of equivalent ways
for forming the GTS for the reversed reaction.
Polyrate 309
14. GENERAL DESCRIPTION OF LCT FILES
In the calculation of LCT probabilities, relevant quantities such as theta integrals (i.e.,
imaginary action integrals) are evaluated on the grid defined by the input parameters
NQTH and NGTHETA. The stored information is then used for interpolation. When extra
output of the LCT calculations is chosen (LCTDETAIL keyword), the details of the
calculation of these quantities at certain grid points, which are specified by user, are
given in files poly.fu41 through poly.fu47. The contents of each output file are listed in
the table below. In the table, 'each tunneling path' refers to a tunneling path
corresponding to an energy quadrature point, IE, that is within the range specified in the
keyword LCTDETAIL in the TUNNEL section of unit fu5 input.
File name Fortran
Unit Contents
poly.fu41 fu41 the theta integrand and the weighting factor at each point
on each tunneling path, within its adiabatic region.
poly.fu42 fu42 the theta integrand, the effective potential, the classical
potential, and the potential correction terms, for each
point on each tunneling path, in its non-adiabatic region
poly.fu43 fu43 the theta integrals and the boundaries of the nonadiabatic
region of each tunneling path
poly.fu44 fu44 the length of the tunneling path
poly.fu45 fu45 the corresponding s value on the MEP for each point on
each tunneling path
poly.fu46 fu46 the adiabatic potential and the cosine of the angle
between the tunneling path and the gradient vector of the
MEP at the s value to which the point on the tunneling
path corresponds for each point on each tunneling path
poly.fu47 fu47 the vibrational turning points, the projection onto each
normal mode coordinate, and the curvature components
for each point on each tunneling path
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Part V More General Program Package Information
15. INSTALLING AND USING POLYRATE
A step-by-step procedure for installing, testing, and using Polyrate is given in this
section. The file structure and the Perl and C Shell scripts should make Polyrate
reasonably easy to install, test, and use.
Subsection 15.A discusses running Polyrate in a Unix environment, including Linux.
Subsection 15.B contains information for users who do not wish to use the provided Unix
scripts or who wish to run Polyrate in a non-Unix environment.
15.A. Instructions for a Unix environment
If the Polyrate program has been received in tar.gz format, the recommended directory
structure will be created automatically when this file is uncompressed and untarred, and
the files will be put in their canonical places as listed in Subsection 15.A.1.
15.A.1. Installation
Before you start, make sure all the file names are in lower case. For the purpose of
illustration, we use upper case for sample directory names, e.g., PDIR. Here PDIR is the
directory above the Polyrate17 directory, i.e., it is the parent directory where you are
going to install POLYRATE.
Polyrate may be downloaded as a single tar.gz file with a structure that is illustrated in
STEP 1. To uncompress and untar the Polyrate tar.gz file in the canonical place the user
has to execute: user@machine [~/Polyrate17] % tar –xzvf Polyrate17.tar.gz
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STEP 1 Verify that the following directory structure was created properly when the file
was uncompressed and untarred. User may use the ‘ls –R’ command.
user@machine [~/Polyrate17] % ls –R
PC/ doc/ obj/ script/ src/ sprng2.0/ testrun/ configure* exe/ poten/ set_machine.jc* testo/ util/ ./PC: check_test.pl poly_ch4cl/ poly_ch5/ poly_cwmc/ poly_hni/ poly_oh3/ clean_test.bat poly_ch4o/ poly_clhbr/ poly_h2ni/ poly_ho2/ poly_ohcl/ clean_update.bat poly_ch4oh/ poly_cmc/ poly_h3/ poly_nh3/ run_all.bat
./PC/poly_ch4cl: poly_ch4cl.mak poly_ch4cl.mdp run_ch4cl.bat ./PC/poly_ch4o: poly_ch4o.mak poly_ch4o.mdp run_ch4o.bat
./PC/poly_ch4oh: run_ch4oh.bat ./PC/poly_ch5: poly_ch5.mak poly_ch5.mdp run_ch5.bat run_lola.bat run_lola.bat.bak
./PC/poly_clhbr: poly_clhbr.mak poly_clhbr.mdp run_clhbr.bat ./PC/poly_cmc: poly_cmc.mak poly_cmc.mdp run_cmc.bat
./PC/poly_cwmc: poly_cwmc.mak poly_cwmc.mdp run_cwmc.bat ./PC/poly_h2ni: poly_h2ni.mak poly_h2ni.mdp run_h2ni.bat
./PC/poly_h3: poly_h3.mak poly_h3.mdp run_h3.bat ./PC/poly_hni: hnitr1.dat hnitr1.fu15 hnitr1.fu6 poly_hni.mak pothni.dat
hnitr1.fu14 hnitr1.fu5 hnitr1.fu61 poly_hni.mdp run_hni.bat ./PC/poly_ho2: poly_ho2.mak poly_ho2.mdp run_ho2.bat ./PC/poly_nh3:
poly_nh3.mak poly_nh3.mdp run_nh3.bat ./PC/poly_oh3: poly_oh3.mak poly_oh3.mdp run_oh3.bat ./PC/poly_ohcl:
poly_ohcl.mak poly_ohcl.mdp run_ohcl.bat
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./doc: ./exe:
./obj: ./poten: c2h7pot5.f ch4o_module.f90 chain4.F coord3.F dumpot.F h3.F ho2.F ohcl.F potch5j2.dat potcwmc3b.dat poth2nilat.dat setup4.F ch3.F ch5.F clhbr.F coord4.F h2ni.F h3_module.F nh3.F potch4o.dat potcmc1.dat potcwmcvib.dat pothni.dat surf3.F
ch4o.F chain3.F cmc.F cwmc.F h2o2.F hni.F oh3.F potch5j1.dat potcmc2.dat poth2niads.dat setup3.F surf4.F ./script: comp_pot.jc* comp_src.jc* exe_chk.jc* link_exe.jc* potcomp.jc*
./src: aamod.f90 dattim.F ef.F fromlapack.F hooks.F intbsv2.F.bak ivtstm.F Makefile polyag.F polymq.F rtpjac.F util.f90 acespoly.F dummy_mpi.F energetics.F givtst.F intbsv1.F intbsv3.F main.F poly31.F polyhl.F polyrr.F sprng_f.h vrctst_mpi.F alloc.f90 dumpot.F fromblas.F headr.F intbsv2.F interface.F main_vrcmpi.F poly40.F poly_mpi.F polysz.F torsion.f90
./src/acesrate: acespoly.F ./src/morate: mopoly.F
./testo: ch3tr1.fu15 ch5fu40tr2.fu15 ch5j1tr2.fu15 cmctr1.fu15 nh3tr1.fu6 oh3tr2.fu15 ch4cltr1.fu15 ch5fu40tr3.fu15 ch5j1tr3.fu15 cmctr2.fu15 nh3tr2.fu15 oh3tr3.fu15 ch4cltr2.fu15 ch5fu40tr4.fu15 ch5j1tr4.fu15 cmctr3.fu15 oh3fu30tr1.fu15 oh3tr4.fu15 ch4ohtr1.fu15 ch5fu40tr5.fu15 ch5j1tr5.fu15 cwmctr1.fu15 oh3fu30tr2.fu15 oh3tr5.fu15
ch4ohtr2.fu15 ch5fu40tr6.fu15 ch5j1tr6.fu15 cwmctr2.fu15 oh3fu30tr3.fu15 oh3tr6.fu15 ch4ohtr3.fu15 ch5fu50tr1.fu15 ch5j1tr7.fu15 cwmctr3.fu15 oh3fu30tr4.fu6 oh3tr7.fu15 ch4ohtr4.fu15 ch5fu50tr2.fu15 ch5j1tr8.fu15 h2nitr1.fu15 oh3fu30tr5.fu6 oh3tr8.fu15 ch4otr1.fu15 ch5fu50tr3.fu15 ch5j1tr9.fu15 h3o2fu31tr1.fu15 oh3fu30tr6.fu15 oh3tr9.fu15 ch5fu29tr1.fu15 ch5fu51tr1.fu15 ch5j2itr1.fu15 h3tr1.fu15 oh3fu31tr1.fu15 ohcltr1.fu15 ch5fu29tr2.fu15 ch5icfu30tr1.fu15 ch5j2itr2.fu15 h3tr2.fu15 oh3fu31tr2.fu15 ohcltr2.fu15
ch5fu30tr1.fu15 ch5icfu30tr2.fu15 ch5j2tr1.fu15 h3tr3.fu15 oh3fu40tr1.fu15 ohcltr3.fu15 ch5fu30tr2.fu15 ch5icfu31tr1.fu15 ch5j2tr2.fu6 h3tr4.fu15 oh3fu40tr2.fu15 ohcltr4.fu15 ch5fu30tr3.fu15 ch5icfu40tr1.fu15 ch5j2tr3.fu15 hnitr1.fu15 oh3fu40tr3.fu15 ohcltr5.fu15 ch5fu30tr4.fu15 ch5icfu40tr2.fu15 clhbrtr1.fu15 ho2tr1.fu15 oh3fu40tr4.fu6 ch5fu30tr5.fu15 ch5j1tr10.fu15 clhbrtr2.fu15 ho2tr2.fu15 oh3fu40tr5.fu6 ch5fu30tr6.fu15 ch5j1tr11.fu15 clhbrtr3.fu15 ho2tr3.fu15 oh3fu40tr6.fu15
ch5fu31tr1.fu15 ch5j1tr12.fu15 clhbrtr4.fu15 ho2tr4.fu15 oh3tr10.fu15 ch5fu40tr1.fu15 ch5j1tr1.fu15 clhbrtr5.fu15 ho2tr5.fu15 oh3tr1.fu15 ./testrun: ch3 ch5 clhbr nh3 runch3.jc runch5.jc runh2ni.jc runho2.jc ch4cl check_all.jc cmc h3 h3o2 oh3 runch4cl.jc runclhbr.jc runh3o2.jc runnh3.jc
ch4o check_test.jc cwmc hni ohcl runch4oh.jc runcmc.jc runh3.jc runoh3.jc ch4oh clean_up.jc h2ni ho2 run_all.jc runch4o.jc runcwmc.jc runhni.jc runohcl.jc ./testrun/ch3:
Polyrate 313
ch3tr1.dat ch3tr1.jc ./testrun/ch4cl: ch4cltr1.dat ch4cltr1.fu29 ch4cltr1.jc* ch4cltr2.dat ch4cltr2.fu29 ch4cltr2.jc*
./testrun/ch4o: ch4otr1.dat ch4otr1.jc* ./testrun/ch4oh: ch4ohic.dat ch4ohiv.dat ch4ohiv2.dat ch4ohtr1.dat ch4ohtr1.jc* ch4ohtr2.dat ch4ohtr2.fu29
ch4ohtr2.jc* ./testrun/ch5: ch5fu29tr1.dat ch5fu30tr5.fu30 ch5fu40tr4.jc* ch5icfu30tr1.dat ch5icfu40tr2.jc* ch5j1tr7.dat ch5fu29tr1.fu29 ch5fu30tr5.jc* ch5fu40tr5.dat ch5icfu30tr1.fu30 ch5j1tr1.dat ch5j1tr7.jc* ch5fu29tr1.jc* ch5fu30tr6.dat ch5fu40tr5.fu40 ch5icfu30tr1.fu50 ch5j1tr1.jc* ch5j1tr8.dat
ch5fu29tr2.dat ch5fu30tr6.fu30 ch5fu40tr5.jc* ch5icfu30tr1.jc* ch5j1tr10.dat ch5j1tr8.jc* ch5fu29tr2.fu29 ch5fu30tr6.jc* ch5fu40tr6.dat ch5icfu30tr2.dat ch5j1tr10.jc* ch5j1tr9.dat ch5fu29tr2.jc* ch5fu31tr1.dat ch5fu40tr6.fu40 ch5icfu30tr2.fu30 ch5j1tr11.dat ch5j1tr9.jc* ch5fu30tr1.dat ch5fu31tr1.fu31 ch5fu40tr6.jc* ch5icfu30tr2.fu50 ch5j1tr11.jc* ch5j2itr1.dat ch5fu30tr1.fu30 ch5fu31tr1.jc* ch5fu50tr1.dat ch5icfu30tr2.jc* ch5j1tr12.dat ch5j2itr1.fu29 ch5fu30tr1.jc* ch5fu40tr1.dat ch5fu50tr1.fu50 ch5icfu31tr1.dat ch5j1tr12.jc* ch5j2itr1.jc*
ch5fu30tr2.dat ch5fu40tr1.fu40 ch5fu50tr1.jc* ch5icfu31tr1.fu31 ch5j1tr2.dat ch5j2itr2.dat ch5fu30tr2.fu30 ch5fu40tr1.jc* ch5fu50tr2.dat ch5icfu31tr1.fu50 ch5j1tr2.jc* ch5j2itr2.fu29 ch5fu30tr2.jc* ch5fu40tr2.dat ch5fu50tr2.fu50 ch5icfu31tr1.jc* ch5j1tr3.dat ch5j2itr2.jc* ch5fu30tr3.dat ch5fu40tr2.fu40 ch5fu50tr2.jc* ch5icfu40tr1.dat ch5j1tr3.jc* ch5j2tr1.dat ch5fu30tr3.fu30 ch5fu40tr2.jc* ch5fu50tr3.dat ch5icfu40tr1.fu40 ch5j1tr4.dat ch5j2tr1.jc* ch5fu30tr3.jc* ch5fu40tr3.dat ch5fu50tr3.fu50 ch5icfu40tr1.fu50 ch5j1tr4.jc* ch5j2tr2.dat
ch5fu30tr4.dat ch5fu40tr3.fu40 ch5fu50tr3.jc* ch5icfu40tr1.jc* ch5j1tr5.dat ch5j2tr2.jc* ch5fu30tr4.fu30 ch5fu40tr3.jc* ch5fu51tr1.dat ch5icfu40tr2.dat ch5j1tr5.jc* ch5j2tr3.dat ch5fu30tr4.jc* ch5fu40tr4.dat ch5fu51tr1.fu51 ch5icfu40tr2.fu40 ch5j1tr6.dat ch5j2tr3.jc* ch5fu30tr5.dat ch5fu40tr4.fu40 ch5fu51tr1.jc* ch5icfu40tr2.fu50 ch5j1tr6.jc* ./testrun/clhbr:
clhbrtr1.dat clhbrtr2.dat clhbrtr3.dat clhbrtr4.dat clhbrtr5.dat clhbrtr1.jc* clhbrtr2.jc* clhbrtr3.jc* clhbrtr4.jc* clhbrtr5.jc* ./testrun/cmc: cmcic.dat cmctr1.dat cmctr1.jc* cmctr2.dat cmctr2.jc* cmctr3.dat cmctr3.fu51 cmctr3.jc*
./testrun/cwmc: cwmctr1.dat cwmctr1.jc* cwmctr2.dat cwmctr2.jc* cwmctr3.dat cwmctr3.jc* ./testrun/h2ni: h2nitr1.dat h2nitr1.jc*
./testrun/h3o2: h3o2fu31tr1.dat h3o2fu31tr1.jc h3o2fu31tr1.fu31 ./testrun/h3: h3tr1.dat h3tr1.jc* h3tr2.dat h3tr2.jc* h3tr3.dat h3tr3.jc* h3tr4.dat h3tr4.jc*
./testrun/hni: hnitr1.dat hnitr1.jc* ./testrun/ho2:
Polyrate 314
ho2ic.dat ho2tr1.jc* ho2tr2.jc* ho2tr4.dat ho2tr5.dat ho2tr1.dat ho2tr2.dat ho2tr3.dat ho2tr3.jc* ho2tr4.jc* ho2tr5.jc* ./testrun/nh3:
nh3ic.dat nh3tr1.dat nh3tr1.jc* nh3tr2.dat nh3tr2.jc*
./testrun/oh3: oh3fu30tr1.dat oh3fu30tr4.dat oh3fu30tr7.dat oh3fu40tr1.dat oh3fu40tr4.dat oh3tr1.dat oh3tr3.jc* oh3tr8.dat oh3fu30tr1.fu30 oh3fu30tr4.fu30 oh3fu30tr7.fu30 oh3fu40tr1.fu40 oh3fu40tr4.fu40 oh3tr1.jc* oh3tr4.dat oh3tr8.jc*
oh3fu30tr1.jc* oh3fu30tr4.jc* oh3fu30tr7.jc* oh3fu40tr1.jc* oh3fu40tr4.jc* oh3tr10.dat oh3tr4.jc* oh3tr9.dat oh3fu30tr2.dat oh3fu30tr5.dat oh3fu31tr1.dat oh3fu40tr2.dat oh3fu40tr5.dat oh3tr10.jc* oh3tr5.dat oh3tr9.jc* oh3fu30tr2.fu30 oh3fu30tr5.fu30 oh3fu31tr1.fu31 oh3fu40tr2.fu40 oh3fu40tr5.fu40 oh3tr11.dat oh3tr5.jc* tr7old.fu30
oh3fu30tr2.jc* oh3fu30tr5.jc* oh3fu31tr1.jc* oh3fu40tr2.jc* oh3fu40tr5.jc* oh3tr11.jc* oh3tr6.dat oh3fu30tr3.dat oh3fu30tr6.dat oh3fu31tr2.dat oh3fu40tr3.dat oh3fu40tr6.dat oh3tr2.dat oh3tr6.jc* oh3fu30tr3.fu30 oh3fu30tr6.fu30 oh3fu31tr2.fu31 oh3fu40tr3.fu40 oh3fu40tr6.fu40 oh3tr2.jc* oh3tr7.dat
oh3fu30tr3.jc* oh3fu30tr6.jc* oh3fu31tr2.jc* oh3fu40tr3.jc* oh3fu40tr6.jc* oh3tr3.dat oh3tr7.jc* ./testrun/ohcl: ohcltr1.dat ohcltr1.jc* ohcltr2.dat ohcltr2.jc* ohcltr3.dat ohcltr3.jc* ohcltr4.dat ohcltr4.jc*
./util: ch4.mi dattim.altix dattim.f dattim.ibm detmi.doc findl.f reord30.f ch4oh.mi dattim.compaq dattim.f90 dattim.iris detmi.f hrotor.doc rotate/ cwmc.rmi dattim.cray dattim.gnu dattim.linux detmi.jc* hrotor.f dateclock.c dattim.dec dattim.hp dattim.sun findb.f oh.mi
./util/rotate: rotate.doc rotate30/ rotate31/ rotate40/ ./util/rotate/rotate30: rotate30.f rotate30.jc* test30.dat test30.fu30
./util/rotate/rotate31: rotate31.f rotate31.jc* test31.dat test31.fu31 ./util/rotate/rotate40: rotate40.f rotate40.jc* test40.dat test40.fu40
STEP 2 Change your working directory to the Polyrate17 directory and run the script
configure by typing ./configure <Return>. You will be asked if you want this
version to be your default version of POLYRATE. If you select yes, then the
hidden files .poly_path and .poly_ver will point to the location and the version
Polyrate 315
of POLYRATE, respectively that you are installing. Then the script will ask
which kind of executable (RP-VTST or VRC-VTST) the Makefile to generate.
You should input your choice, i.e., “RP” or “VRC”. Next, the script will
automatically detect available C and FORTRAN compilers and ask if you want to
use the detected options. Usually, you should answer “yes” so that you can use
the automatically detected compilers. If you want to use a different compiler,
you should do the followings: (step 1) answer “yes” and proceed with the
current configuring; (step 2) go to src/ directory, and open the Makefile; (step
3) At the beginning of the Makefile, you will see:
F77C = /usr/bin/gfortran -O -fno-automatic
CC = /usr/bin/gcc
Please change the definition of these two variables (F77C and CC) to the
location of your fortran and C compilers.
Note that no executable file is generated in this configuration step and the
generated Makefile is for either RP-VTST or VRC-VTST.
STEP 3 Check the Makefile to ensure that the correct compiler options appear.
POLYRATE17 supports dynamic memory but previous versions do not, so
compiler options that force static memory are typically required for previous
versions. For example, the g77 compiler requires the flag ‘-fno-automatic’,
and the Portland Group compiler requires the flag ‘-Msave’. Due to the
various combinations of OS and compilers, the configure script does not
always print these flags automatically.
STEP 4 You may proceed directly to testing. The Makefile will compile any files that
are needed to execute the test runs. If you want to use your own potential
energy surface, you have to add it to the Makefile. The name of the new
executable, the file name of the potential energy surface and its object have to
be added. Comments in the Makefile will help you make these additions.
Polyrate 316
STEP 5 The following two compiling problems are common enough to merit special
mention. If you get an error relating to module libc.a(shr.o), it is probably
because other modules are interfering with the compilation. Unload any extra
modules that are running and recompile. If during the compilation of the RP-
VTST version, the installation stops because the file mpif.h cannot be found,
the user should generate a dummy file called mpif.h in the src directory (for
instance, by typing touch mpif.h <Return> in the Polyrate src directory).
.
15.A.2. Testing
The directory structure and files should be set up as instructed in Subsection 15.A.1.
Note that some of the processes described in this section may be time consuming. In a
Unix system, you can always add an ‘&’ character at the end of a command line to put
the process in the background. In the following instructions, whenever you see a
command followed by an ‘&’ character, it means that we suggest that the user run the
command in the background.
It is recommended that the user run all the test runs in the distribution package before
using POLYRATE. We have included many useful scripts to run the test runs, and you can
choose how to run the test runs from among several different approaches.
(1) To run all the test runs:
The test runs are grouped into 15 different sets, in particular, ch3, ch4cl, ch4oh, ch5,
clhbr, cmc, cwmc, h2ni, h3, h3o2, hni, ho2, nh3, oh3, and ohcl test runs. (See Subsection
16.C.) Each set has its own subdirectory in the Polyrate17/testrun directory. (See
Subsection 15.A.1.) The subdirectories contain the input data files and the job control
files for the test runs. The only thing you need to run all the test runs for either RP-VTST
or VRC-VTST is to change the working directory to the Polyrate17/testrun directory and
run the script run_allRPVTST.jc or run_allVRCVTST.jc.
./run_allRPVTST.jc & <Return>
(or submit it as a batch job)
Polyrate 317
Note run_allRPVTST.jc and run_allVRCVTST.jc need different Makefiles.
The user has to take the steps described in Section 15.A.1 to generate a Makefile either
for VRC-VTST calculations or for RP-VTST calculations.
(2) To run a subset of the test runs
1. To run a set of test runs, use the scripts available in the testrun/ directory. For
example, to run all the h3 test runs, change the working directory to the
Polyrate17/testrun directory and use the script runh3.jc.
(change to the testrun/ directory)
./runh3.jc & <Return>
(or any of the other run{name}.jc scripts, where {name} can be ch5, oh3, ho2,
clhbr, cmc, cwmc, nh3, hni, h2ni, ch4cl, or ch4oh)
3. To run an individual test run, say ch5j1tr1, change the directory to testrun/ch5/
and use the script ch5j1tr1.jc.
./ch5j1tr1.jc & <Return>
(or any of the {test_run_name}.jc scripts in that directory)
Note: Do not run more than one test run in the same directory simultaneously.
(See Subsection 15.B, item VI.)
(3) To check the test run results:
When you finish running the test runs, you should check if they produced the correct
results by comparing the test run short output files (fu15 files) with the ones in the testo/
directory. There is a useful script, check_test.jc, in the testrun/ directory to do this after
you finish a whole set of test runs. For example, if you have finished all the oh3 test runs
and you want to compare the results with the correct ones, change the working directory
to testrun/ and type ./check_test.jc oh3 <Return>. The script will use the Unix command
diff to compare your results with the ones in the directory testo/, and generate an output
file called oh3.chk. You can then look at the contents of that file and see if there are any
differences. Since the reaction rates are not calculated in test runs ch5j2tr2 and nh3tr1,
the short output files for these two test runs are not created. Thus if you type
check_test.jc ch5 <Return>, there will be no check for ch5j2tr2. You can still use the diff
Polyrate 318
command to compare the long output files (fu6 files) of these test runs with the ones
provided in the Polyrate17/testo directory. There is a similar script, check_all.jc, that
you can use to test the full suite of test runs.
If your test runs reproduce the results in Polyrate17/testo, the only differences will be the
date and time. Otherwise, the script will point out where the results differ from each
other. (Of course, you have to know a little bit about the diff command to understand its
output. Type man diff <Return> if you need help.) In running the test runs on different
machines, we found that the differences in the rate constants were never greater than 1%.
If your rate constant results do not differ from the ones in the Polyrate17/testo directory
by more than this percentage, they are probably correct; otherwise, something unexpected
might be happening.
(4) Cleaning up:
When you finish checking the testrun results, you may want to clean up the testrun
directory to save disk space. The script, clean_up.jc, in the Polyrate17/testrun directory
can be used to remove all the files Polyrate generated when running the test suite. These
files include the following: *.fu1, *.fu6, *.fu14, *.fu15, *.fu25, *.fu26, *.fu27, and
*.fu61.
15.A.3. Using POLYRATE
Many users will user Polyrate mainly as part of a direct dynamics calculations carried out
with GAMESSPLUSRATE, GAUSSRATE, JAGUARRATE, MC-TINKERATE, MORATE,
MULTILEVELRATE, or NWCHEMRATE. However the rest of this section is devoted to using
Polyrate as a stand-alone program.
After installation you should have the default directory structure and the correct machine-
dependent files. If you are planning to use Polyrate with a direct dynamics code, such as
GAUSSRATE or MULTILEVELRATE, read the instructions in the direct dynamics manual. If
you are planning to use Polyrate as a stand-alone code, follow the instructions in this
section:
1. Unless you are performing an electronic structure input file calculation, prepare
your own potential energy surface subroutine to do the calculations. See Section 8
Polyrate 319
for a discussion of user-supplied potential energy surfaces. Supposing that you have
made your own potential energy surface subroutine, you need to compile it before
you link it with the Polyrate source code. This can be accomplished by adding the
surface into the Makefile located in the src directory. Comments in the Makefile
will show you where to add lines. For example, suppose you have made a surface
subroutine for a system that consists of 2 hydrogen atoms and 1 oxygen atom, and
you have put it in the Polyrate17/poten directory and named oh2.f. You have to
add the following line where the executables are defined
OH2S = ../exe/Polyrate$(VERSION).oh2.serial.exe
Then add ../poten/oh2.f to the POT: list, using a \ in order to continue a
line. Also, add the following line to compile the surface, beginning with a tab.
$(F77C) -c ../poten/oh2.f
Finally, add the lines that create the executable. Use a tab to start the second line.
OH2S:$(OBJ) dummy_mpi.o oh2.o
$(F77C) -o $(OH2) $(OBJ) dummy_mpi.o oh2.o
For three- and four-atom systems, the user can take advantage of some pre-written
subroutines, namely: setup, surf, coord, and chain. If these subroutines were not
explicitly included in the oh2.f file, the lines to create the executable would look
like this (without a break between oh2.o and setup3.o):
OH2S:$(OBJ) dummy_mpi.o oh2.o
$(F77C) -o $(OH2) $(OBJ) dummy_mpi.o oh2.o
setup3.o surf3.o coord3.o chain3.o
2. Prepare the input data files. Study Section 12 carefully to make the input data files
correctly. Because some of the input data files are quite complicated, it may be
easier to use some of the test run input data files as templates when preparing your
own input data files.
Polyrate 320
3. Run the dynamics calculations with POLYRATE. After you finish steps 1 and 2, you
are ready to use Polyrate to do your calculations. Before you submit your job to the
computer, it is recommended that you do the following:
A. Make a directory for each specific reaction. For example, you can make a directory
called reaction in the Polyrate17 directory or somewhere else, and when you are
planning to do a calculation on a specific reaction, say O + H2, you can create a
directory called oh2 in the Polyrate17/reaction directory. You can then use this
directory as your working directory for this reaction and put all the input data files
and output files in this directory.
B. Use a job control script (.jc) to handle all the processes involved in running
POLYRATE. Polyrate only recognizes a certain set of input file names and will
generate a set of output files with certain names (see Sections 12, 15.B and 16.C),
therefore, the user always needs to copy (or link) the input data files to the default
names and rename the output files to more logical names. It is more convenient to
use a script to control these tedious processes. Using a script also makes it easier to
run the job in background or to submit the Polyrate run as a batch job. In fact, we
have included job control files for all test runs in the distribution package. You
probably used them when you ran the test runs, and you can easily modify them for
your own needs. They all reside in the subdirectories of the Polyrate17/testrun
directory. In your .jc script, be sure to change the ‘set name’ and ‘gmake’ lines to
match your job. In the OH2 example, if you decided the name your files oh2run1,
the lines would look like this:
set name = oh2run1
gmake OH2S
C. With gmake in the job control script, the executable will be compiled the first time
that it is used, and also anytime there is a change in one of the files that it is
dependent on. If a change is made to the source code, the next time that the job
control script is run, gmake will recognize that a change has been made and compile
the changed code and create a new executable. If the user does not desire this
feature, the gmake line may be deleted from the .jc job control script once the
Polyrate 321
executable is compiled for the first time. Executables are put in the exe directory
by default.
15.B. Comments for expert users
Of course, users need not use the provided Unix scripts, files, or recommended
directory structure. All that is needed is the compilation of the source code, linking the
Polyrate object files with appropriate potential energy surface object file(s), and running
the executable file(s) with input data file(s). However, there are a few practical issues to
be aware of, as follows.
Compilation of POLYRATE
For the RP version of the code, compile
dattim.F ef.F fromlapack.F hooks.F intbsv2.F.bak ivtstm.F,
polyag.F polymq.F rtpjac.F util.f90 acespoly.F dummy_mpi.F
energetics.F givtst.F, intbsv1.F intbsv3.F main.F poly31.F
polyhl.F polyrr.F sprng_f.h vrctst_mpi.F, alloc.f90 dumpot.F
fromblas.F headr.F intbsv2.F interface.F main_vrcmpi.F
poly40.F , poly_mpi.F polysz.F torsion.f90
For the RP version of the code compile
energetics.F, givtst.F, hooks.F, intbsv1.F, intbsv2.F intbsv3.F,
interface.F, main.F, Polyrate.F, polyag.F, polyhl.F, polymq.F, polyrr.F,
polysz.F, rtpjac.F,
The POLYRATE17 program should be compiled with 64-bit precision and dynamic
memory allocation.
Compilation of the potential energy surface files
The potential energy surface subroutines provided with the Polyrate program
should be compiled with the same precision and memory specifications used for the
Polyrate source code. Any user-supplied potential energy surface subroutine must also
be compiled with 64-bit precision, but specification for static memory allocation will
depend on the way in which the subroutine is written.
Polyrate 322
Creation of an executable file
Link the Polyrate object file with potential object file(s) to create specific
POLYRATE-potential executable file(s).
Running POLYRATE
The Polyrate program opens all the input and output files needed for a calculation
with the logical file names poly.fu#, where # is an integer. The files poly.fu5 and
poly.fu6 are always opened (they correspond to input and output files respectively). The
other poly.fu# files are opened depending on which options are set. Therefore, all the
necessary input data files must be copied or linked to files with the proper logical names.
If the user wants the output files to have different names, the renaming of the poly.fu#
output files must be performed after the calculation has completed.
Note: Because the Polyrate program opens and closes its files with the file name
specification poly.fu#, these files should be renamed at the end of each calculation, or
there will be conflicts when two calculations are run in the same directory.
In addition to the Polyrate input and output files, the user should ensure that the
potential data files, if any, which are opened by the potential energy surface
subroutine(s), have the correct file names as specified in the OPEN statement(s) in the
potential subroutine source code. For the test runs, these names are listed after "FILE
NAME =" in Subsection 16.C. Also, these data files need to be in the working directory
of the calculation.
15.C. Running in parallel using MPI
The Polyrate program has been expanded to work with multiple processors using MPI.
MPI can be very machine dependent, therefore this section will highlight the areas that
need to be correct for the parallel feature to work correctly. There are two MPI versions.
One is for calculations with MEP and the other one is for calculations with variable
reaction coordinate (VRC). These two versions need to be compiled by including
different subroutines since they use different parallel schemes.
A. MPI version for calculations with MEP
Polyrate 323
For samples on how to make MPI work using MEP, see the CH5P sections of the
Makefile, and look at the job control scripts in the ch5 testruns. The MPI sections of the
Makefile are only printed if an MPI compiler is found by the configure script.
I. In the Makefile, MPIF77C needs to be set to the correct MPI compiler. The
poly_mpi.f source file must be compiled using this compiler, not the serial
compiler. Finally, the linking section must use the MPI compiler when creating
the executable.
II. In the job control script (*.jc file), set $nproc equal to the number of processors
you wish to use. Make sure the exe variable is set to the proper executable. Most
importantly, the platform on which you are running has a certain way that MPI
jobs must be run. By default, the line looks like this:
(time mpirun -v -np $nproc $exe) >>& $name.time
where “mpirun -v -np $nproc $exe” is the part that actually tells the
program how to run. This line will likely need to be edited to work with each
platform.
III. For an example, the testrun ch5j1tr1 has edited this line in the job control script to
work on a particular IBM regatta. The line now reads:
(time poe $exe -rmpool 1 -nodes 1 -procs
$nproc) >>& $name.time
B MPI version for calculations with VRC
When installing Polyrate program, user will be asked whether the MPI executable for
variable reaction coordinate need to be compiled by a Perl installation script under
Polyrate17 directory, named configure. This script will automatically search MPI
compiler for user. But user has to be responsible to make sure the compiler and its
options are correct in Makefile since MPI can be very machine dependent.
Polyrate 324
Since this MPI version for variable reaction coordinate use SPRNG (SCALABLE PARALLEL
RANDOM NUMBER GENERATOR LIBRARY) package in Monte Carlo integrations, user needs
to install SPRNG before Polyrate installation. Starting with version 2010, SPRGN 2.0
package is included in Polyrate program. The Polyrate installation script will compile the
SPRNG 2.0 library before generate Makefile for VRC-VTST run. The SPRNG package can
also be downloaded from its website at the Florida State University
(http://sprng.cs.fsu.edu/) and installed separately by users. When linking object files, user
should give the correct path for SPRNG library by changing the $SPRNGLIB variable in
Makefile if user desires use separately installed SPRNG library.
Polyrate 325
16. SAMPLE TEST RUNS
16.A. Chart of the potential energy functions and data files
The following chart gives the name of the potential energy function and data file(s) that
are used for each test run. They are files located in the Polyrate17/poten directory.
When two data files are listed for the same test run, both data files are required. The file
listed first should be assigned to unit 4, and the file listed second should be assigned to
unit 7.
TEST RUN(S) POTENTIAL SOURCE CODE POTENTIAL DATA FILE(S)
ch3tr1 ch3.F (none)
ch5j1tr1-ch5j1tr11 ch5.F potch5j1.dat
ch5j2tr1-ch5j2tr3 ch5.F potch5j2.dat
ch5fu51.tr1 ch5.F potch5j1.dat
clhbrtr1-clhbrtr4 clhbr.F (none)
cmctr1, cmctr2 cmc.F potcmc1.dat
potcmc2.dat
cwmctr1-cwmctr3 cwmc.F potcwmc3b.dat
potcwmcvib.dat
TEST RUN(S) POTENTIAL SOURCE CODE POTENTIAL DATA FILE(S)
ch4otr1 ch4o.F potch4o.dat
potch4o.inc
h3tr1-h3tr4 h3.F (none)
nh3tr1–nh3tr2 nh3.F (none)
ho2tr1–ho2tr5 ho2.F (none)
oh3tr1–oh3tr10 oh3.F (none)
hnitr1 hni.F pothni.dat
h2nitr1 h2ni.F poth2niads.dat
poth2nilat.dat
ohcltr1-ohcltr4 ohcl.F (none)
16.B. Descriptions of sample test runs
Polyrate 326
This section contains descriptions of the sample runs which make up the Polyrate test
suite. The input data files and the summary output files from unit fu15 for the test runs
are part of the distribution package. For convenience, we have named all the test runs
according to the potential energy surface used for the test run.
The following is a list of reactions involved in the test suite and references to published
calculations of their reaction rates using POLYRATE.
CH3 + H2 → CH3
CH3 + H2 → CH4 + H see Refs. 17 and 20 in Sect. 21
CH3 + HPh → CH4 + Ph see Ref. 21 in Sect. 21
Cl + HBr → ClH + Br see Ref. 10 in Sect. 21
Cl- + CH3Cl' → ClCH3 + Cl'- see Ref. 23 in Sect. 22
Cl-(H2O) + CH3Cl' → ClCH3 + Cl'-(H2O) see Ref. 24 in Sect. 22
H2 + H' → HH' + H see Ref. 12 in Sect. 21
OH + O → HO2 see Ref. 4 in Sect. 21
O2 + H → HO2 see Ref. 4 in Sect. 21
NH3 → NH3 (inversion) see Ref. 7 in Sect. 21
OH + H2 → H2O + H see Refs. 1, 3, and 6 in Sect. 21
H(a)/Ni(100) → H(a)/Ni(100) see Ref. 33 in Sect. 22
H2(a)/Ni(100) → 2H(a)/Ni(100) see Ref. 19 in Sect. 21
OH + CH4 → H2O + CH3 see Refs. 26 and 32 in Sect. 21
Cl + CH4 → HCl + CH3 see Refs. 22 and 26 in Sect. 21
CH4 + O → CH3 + OH see Ref. 52 in Sect. 22
O + HCl → OH + Cl
Polyrate 327
O + HCl(v=1) → OH + Cl see Refs. 22 and 26 in Sect. 21
H2O2 + H → H2O + OH
Various options were used for each of these systems to give a thorough test of POLYRATE.
Some of the most critical options used are discussed in each description; the keywords
used for these options are specified in square brackets: e. g. [KEYWORD]. The potential
energy surfaces used for the sample runs for the reaction CH3 + H2 → CH4 + H are
surfaces J1 and J2 of Joseph et al. [Ref. 17, Sect. 21]. Surface J1 is also used for the
calculations for the reaction CH3 + HPh → CH4 + Ph, where Ph denotes a single atom
with the mass of a phenyl group (see Ref. 21 in Sect. 21). The calculations for the
reaction Cl + HBr → ClH + Br use the extended LEPS surface of Babamov, Lopez, and
Marcus [Ref. 26, Sect. 22]. The calculations for the Cl-(H2Om) + CH3Cl' → ClCH3 +
Cl'-(H2Om) reactions, m = 0,1, use the potential energy surface of Tucker and Truhlar
[Ref. 23, Sect. 22] and Zhao et al. [Refs. 24 and 27, Sect. 22], while the DMBE surface of
Varandas et al. [Ref. 28, Sect. 22] is used for the reaction H2 + H' → HH' + H. The
calculations for the reaction OH + O → HO2 and O + H2 → HO2 use the ab initio surface
of Melius and Blint [Ref. 29, Sect. 22], and all the runs for the reaction OH + H2 → H2O
+ H use the Schatz-Elgersma fit to the Walch-Dunning ab initio potential energy surface
[Refs. 30 and 31, Sect. 22]. The embedded diatomics-in-molecules (EDIM) potential
with parameter set 4 of Truong et al. [Refs. 25 and 32, Sect. 22] is used for the H/Ni(100)
surface diffusion test run, and the Lee and DePristo [Ref. 33, Sect. 22] potential energy
surface, as modified by Truong et al. [Ref. 19, Sect. 21], is used for the H2/Ni(100)
system. Furthermore, both Ni surface test runs are carried out assuming that the entire
metallic subsystem on which the diatoms are absorbed is rigid. The calculations for the
reaction Cl- + CH3Cl' → ClCH3 + Cl'- use the semiempirical surface of Tucker and
Truhlar [Ref. 23, Sect. 22], and the calculations for the NH3 inversion use potential
energy surface II of Brown, Tucker, and Truhlar [Ref. 7, Sect. 21]. For the OH + CH4 →
H2O + CH3 [Ref. 32, Sect. 21] and Cl + CH4 → HCl + CH3 [Ref. 22, Sect. 21] reactions,
rate calculations are carried out using the IVTST method [Ref. 26, Sect. 21] with ab initio
data.
It should be pointed out that the results for the ClHBr and the H3 test runs will differ
from the published results. This difference occurs because the published results for those
systems were determined using another program, ABCRATE, which calculates
Polyrate 328
anharmonicity corrections differently than POLYRATE. In particular, ABCRATE uses
curvilinear internal coordinates, and these produce quite different harmonic frequencies,
as discussed elsewhere [Ref. 25 and 41, Sect. 21].
Note that the test runs are designed to illustrate the use of the Polyrate program. No
implication is made that these runs are converged with respect to all step sizes and grid
ranges. One can use these runs to test that the code as received gives the same results on
various new platforms by comparing the output for these test runs to the distributed
output, even though the results are not necessarily converged with respect to numerical
parameters.
Polyrate 329
16.C.1. Test run ch5j1tr1
CH3 + H2 → CH4 + H with harmonic approximation
This sample run is for the reaction CH3 + H2 → CH4 + H with the J1 potential energy
surface. All normal modes and generalized normal modes are treated using the default
harmonic approximation. The rate constants are computed using CVT and ICVT [CVT,
ICVT]. Tunneling corrections are computed using the MEPSAG, CD-SCSAG, and LCG3
methods [ZCT, SCT, SCTOPT, LCTOPT] Note that only the ground-state in the LCG3 exit
arrangement is considered for the LCG3 calculation in this run [NOALLEXCIT] this option
is chosen to simplify the calculation because we expect on physical grounds that only
ground-state-to-ground-state tunneling is important in this case. The LCT keyword was
not explicitly given since the default is on when LCTOPT is used. The rate constants are
computed for ten temperatures [TEMP], and the activation energies are computed for six
pairs of temperatures [EACT]. The MEP is followed using the Page-McIver method [RPM
= pagem] with a step size of 0.001 bohr [SSTEP]. The Hessian matrix is recalculated and
a mode analysis is performed every 0.01 bohr [INH = 100]. The curvature components
are calculated using a quadratic fit to obtain the derivative of the gradient with respect to
the reaction coordinate [CURV = dgrad]. A restart file containing reaction-path
information is written to unit fu1 [RESTART = writefu1] for use in test run ch5j1tr2.
For both reactants and the first product STATUS = 6 and the geometries, energies, and
frequencies are read from fu5, for the second product STATUS = 2 and the geometry is
read from fu5, and for the saddle point STATUS = 4 and the geometry, energy, and
Hessian are read from fu5. The reactants are input in fu5 [ENERGY, FREQ] to reduce the
number of calculations. The results may be compared to those in Table VII of Ref. 17 in
Sect. 21.
Polyrate 330
Polyrate I/O FILES
FILE NAME Polyrate FILE NAME
ch5j1tr1.dat poly.fu5 input data file
ch5j1tr1.fu6 poly.fu6 long output file
ch5j1tr1.fu1 poly.fu1 reaction path info.
ch5j1tr1.fu14 poly.fu14 summary output file
ch5j1tr1.fu15 poly.fu15 summary output file
ch5j1tr1.fu61 esp.fu61 2nd restart option file
POTENTIAL ENERGY SURFACE DATA FILE
potch5j1.dat UNIT = 4
FILE NAME = potch5.dat
Polyrate 331
16.C.2. Test run ch5j1tr2
CH3 + H2 → CH4 + H with harmonic approximation
This sample run is for the reaction CH3 + H2 → CH4 + H with the J1 potential energy
surface. All the parameters are the same as for test run ch5j1tr1 except that the reaction-
path information is read from a restart file on unit fu1 [RESTART: readfu1]. In order to
perform this test run, the restart file must first be created by the user by running test run
ch5j1tr1.
Polyrate I/O FILES
FILE NAME Polyrate FILE NAME
ch5j1tr2.dat poly.fu5 input data file
ch5j1tr1.fu1 poly.fu1 reaction path info.
(input data for a
restart calculation)
ch5j1tr2.fu6 poly.fu6 long output file
ch5j1tr2.fu14 poly.fu14 summary output file
ch5j1tr2.fu15 poly.fu15 summary output file
POTENTIAL ENERGY SURFACE DATA FILE
potch5j1.dat UNIT = 4
FILE NAME = potch5.dat
Polyrate 332
16.C.3. Test run ch5j1tr3
CH3 + H2 → CH4 + H with mass-weighted reaction coordinate
This sample run for the reaction CH3 + H2 → CH4 + H is similar to test run ch5j1tr1,
except that the reduced mass [SCALEMASS] which defines the mass-scaled Cartesian
coordinates, is set equal to the default, 1.0 amu. Thus, these coordinates have the same
numerical values as the conventional mass-weighted coordinates in infrared
spectroscopy. The vibrational partition functions are multiplied by a factor of 1 1010 to
avoid underflow [VPFEXP] ; note that these changes alone would not change the final rate
constants. In addition, though, in this run the effective mass for the CD-SCSAG
tunneling calculation is obtained by sixth-order Lagrangian interpolation [SCTOPT:
lagrange] instead of a cubic spline fit. Also, there is no LCG3 calculation in this test run.
Polyrate I/O FILES
FILE NAME Polyrate FILE NAME
ch5j1tr3.dat poly.fu5 input data file
ch5j1tr3.fu6 poly.fu6 long output file
ch5j1tr3.fu14 poly.fu14 summary output file
ch5j1tr3.fu15 poly.fu15 summary output file
POTENTIAL ENERGY SURFACE DATA FILE
potch5j1.dat UNIT = 4
FILE NAME = potch5.dat
Polyrate 333
16.C.4. Test run ch5j1tr4
CH3 + H2 → CH4 + H with harmonic approximation in redundant internal
coordinates and the Page-McIver method to calculate
reaction-path curvature
This sample run for the reaction CH3 + H2 → CH4 + H demonstrates the calculation of
reaction-path curvature components from the Hessian, generalized normal mode
eigenvectors, and gradient [CURV = dhess] using eq. (48) of Page and McIver [Ref. 17,
Sect. 22]. The MEP is followed using the Euler steepest-descents (ESD) method [RPM =
esd] with a step size of 0.0001 bohr [SSTEP]. A generalized normal mode analysis is
performed every 0.01 bohr along the MEP [INH = 100], and all the vibrations are treated
harmonically in redundant internal coordinates [COORD = curv3]. Both CVT [CVT] and
ICVT [ICVT] rate constants are calculated, and tunneling corrections are computed using
both MEPSAG and CD-SCSAG methods [ZCT, SCTOPT] .
Polyrate I/O FILES
FILE NAME Polyrate FILE NAME
ch5j1tr4.dat poly.fu5 input data file
ch5j1tr4.fu6 poly.fu6 long output file
ch5j1tr4.fu14 poly.fu14 summary output file
ch5j1tr4.fu15 poly.fu15 summary output file
POTENTIAL ENERGY SURFACE DATA FILE
potch5j1.dat UNIT = 4
FILE NAME = potch5.dat
Polyrate 334
16.C.5. Test run ch5j1tr5
CH3 + HPh → CH4 + Ph with LCG3 calculation for the ground state only
This sample run is for the CH3 + HPh → CH4 + Ph reaction, where Ph denotes a single
particle with the mass of a phenyl group. The CH5 analytical potential energy surface,
J1, is used for this six-atom model problem; see Ref. 21 in Sect. 21 for further discussion.
All normal modes and generalized normal modes are treated using the default harmonic
approximation. TST, CVT, and ICVT rate constants are computed [TST, CVT, ICVT]. The
tunneling calculations for ground-state transmission coefficients are computed using the
MEPSAG, CD-SCSAG, and LCG3 methods [ZCT, SCTOPT, LCTOPT] . The program writes
a restart file containing the reaction-path information to unit fu1 for use in test run
ch5j1tr6 [RESTART = writefu1]. The MEP is followed using the ESD integrator
without stabilization (ESD method) [RPM = esd] with a step size of 0.0001 bohr [SSTEP],
and a generalized normal mode analysis is performed every 0.01 bohr [INH = 100]. The
curvature components are calculated using a quadratic fit to obtain the derivative of the
gradient with respect to the reaction coordinate [CURV = dgrad] . The results may be
compared to those in Table 5 in Ref. 21 in Sect. 21, but it should be noted that there is a
difference of a few percent between the LCG3 results in Ref. 21 and those calculated
with this data file due to improved convergence.
Polyrate I/O FILES
FILE NAME Polyrate FILE NAME
ch5j1tr5.dat poly.fu5 input data file
ch5j1tr5.fu6 poly.fu6 long output file
ch5j1tr5.fu1 poly.fu1 reaction path info.
ch5j1tr5.fu14 poly.fu14 summary output file
ch5j1tr5.fu15 poly.fu15 summary output file
POTENTIAL ENERGY SURFACE DATA FILE
potch5j1.dat UNIT = 4
FILE NAME = potch5.dat
Polyrate 335
16.C.6. Test run ch5j1tr6
CH3 + HPh → CH4 + Ph with LCG3 calculation for all energetically accessible excited
states from a restart file in which the LCG3 calculation was
carried out for the ground state only; rate constants are also
calculated at more temperatures. (Restart file for unit fu1 is
from test run ch5j1tr5)
This sample run, like the preceding test run, is for the CH3 + HPh → CH4 + Ph reaction,
where Ph denotes a single particle with the mass of a phenyl group. The potential energy
surface and all the parameters are the same as for test run ch5j1tr5 except for the
tunneling calculations and the temperatures for which the rate constants are calculated.
In this run the tunneling calculations for ground-state transmission coefficients are
performed with the MEPSAG, CD-SCSAG, and LCG3 methods [ZCT, SCTOPT, LCTOPT].
For the LCG3 calculation, the program determines the highest excited state of the LCG3
exit arrangement which is accessible, and those excited states are included in the LCG3
calculation [ALLEXCIT]. The results may be compared to those from test run ch5j1tr5, in
which the LCG3 calculations were done for the ground state only; the present LCG3
transmission coefficients are up to 4% larger.
Polyrate I/O FILES
FILE NAME Polyrate FILE NAME
ch5j1tr6.dat poly.fu5 input data file
ch5j1tr5.fu1 poly.fu1 reaction path info.
(input data for a
restart calculation)
ch5j1tr6.fu6 poly.fu6 long output file
ch5j1tr6.fu14 poly.fu14 summary output file
ch5j1tr6.fu15 poly.fu15 summary output file
POTENTIAL ENERGY SURFACE DATA FILE
potch5j1.dat UNIT = 4
FILE NAME = potch5.dat
Polyrate 336
16.C.7. Test run ch5j1tr7
CH3 + H2 → CH4 + H with Page-McIver mass-weighted reaction path and
IVTST0FREQ
This sample run for the reaction CH3 + H2 → CH4 + H is similar to test run ch5j1tr3,
except that the reaction-path curvature components are calculated from the Hessian,
generalized normal mode eigenvectors, and gradient [CURV = dhess] using eq. (48) of
Page and McIver [Ref. 17, Sect. 22]. The MEP is followed using the Page-McIver
method [RPM = pagem] with a step size of 0.001 bohr [SSTEP]. The Hessian matrix is
recalculated and a mode analysis is performed every 0.01 bohr [INH = 100]. The
vibrational partition functions are multiplied by a factor of 1 1010 to avoid underflow
[VPFEXP]; note that this alone would not change the final rate constants. In addition, the
effective mass for the CD-SCSAG tunneling calculation is obtained by sixth-order
Lagrangian interpolation [SCTOPT: lagrange] instead of the default cubic spline fit. Also,
there is no LCG3 calculation in this test run. The IVST0FREQ method [IVTST0FREQ] is
used to modify the 10th and 11th vibrational modes along the reaction path.
Polyrate I/O FILES
FILE NAME Polyrate FILE NAME
ch5j1tr7.dat poly.fu5 input data file
ch5j1tr7.fu6 poly.fu6 long output file
ch5j1tr7.fu14 poly.fu14 summary output file
ch5j1tr7.fu15 poly.fu15 summary output file
POTENTIAL ENERGY SURFACE DATA FILE
potch5j1.dat UNIT = 4
FILE NAME = potch5.dat
Polyrate 337
16.C.8. Test run ch5j1tr8
CH3 + H2 → CH4 + H with MEPSAG and CD-SCSAG calculations at two
temperatures [one of the test cases in Ref. 27 in Sect. 21]
This sample run for the reaction CH3 + H2 → CH4 + H is one of the test cases in Ref. 27
in Sect. 21. (However, Ref. 27 used SCSAG whereas the current code uses CD-SCSAG).
The MEP is calculated from s = -1.3 bohr to s = 0.8 bohr [SRANGE] using the Euler
stabilization method [RPM = es1] . The gradient and save step sizes are all set to 0.047
bohr [SSTEP, INH = 1] The finite difference step size and the tolerance parameter in the
ES1 method are set to 0.072 (1.532*SSTEP) [ES1OPT: delta2] and 0.082 [ES1OPT: DIFFD],
respectively. The CVT/MEPSAG and CVT/CD-SCSAG rate constants are calculated
[CVT, ZCT, SCT] at 200K and 300K [TEMP]. All the rate constants are within 15% of the
converged values obtained in the test run ch5j1tr1.
Polyrate I/O FILES
FILE NAME Polyrate FILE NAME
ch5j1tr8.dat poly.fu5 input data file
ch5j1tr8.fu6 poly.fu6 long output file
ch5j1tr8.fu14 poly.fu14 summary output file
ch5j1tr8.fu15 poly.fu15 summary output file
POTENTIAL ENERGY SURFACE DATA FILE
potch5j1.dat UNIT = 4
FILE NAME = potch5.dat
Polyrate 338
16.C.9. Test run ch5j1tr9
CH3 + H2 → CH4 + H with harmonic approximation
This sample run is for the reaction CH3 + H2 → CH4 + H with the J1 potential energy
surface. All normal modes and generalized normal modes are treated using the default
harmonic approximation. The rate constants are computed using CVT and ICVT [CVT,
ICVT]. Tunneling corrections are computed using the MEPSAG, CD-SCSAG, and LCG4
methods [ZCT, SCT, SCTOPT, LCTOPT] Note that only the ground-state in the LCG4 exit
arrangement is considered for the LCG4 calculation in this run [NOALLEXCIT] this option
is chosen to simplify the calculation because we expect on physical grounds that only
ground-state-to-ground-state tunneling is important in this case. The LCT keyword was
not explicitly given since the default is on when LCTOPT is used. The rate constants are
computed for ten temperatures [TEMP], and the activation energies are computed for six
pairs of temperatures [EACT]. The MEP is followed using the Page-McIver method [RPM
= pagem] with a step size of 0.001 bohr [SSTEP]. The Hessian matrix is recalculated and
a mode analysis is performed every 0.01 bohr [INH = 100]. The curvature components
are calculated using a quadratic fit to obtain the derivative of the gradient with respect to
the reaction coordinate [CURV = dgrad]. For both reactants and the first product STATUS
= 6 and the geometries, energies, and frequencies are read from fu5, for the second
product STATUS = 2 and the geometry is read from fu5, and for the saddle point STATUS =
4 and the geometry, energy, and Hessian are read from fu5. The reactants are input in fu5
[ENERGY, FREQ] to reduce the number of calculations. The results may be compared to
those in Table VII of Ref. 17 in Sect. 21.
Polyrate 339
Polyrate I/O FILES
FILE NAME Polyrate FILE NAME
ch5j1tr9.dat poly.fu5 input data file
ch5j1tr9.fu6 poly.fu6 long output file
ch5j1tr9.fu1 poly.fu1 reaction path info.
ch5j1tr9.fu14 poly.fu14 summary output file
ch5j1tr9.fu15 poly.fu15 summary output file
ch5j1tr9.fu61 esp.fu61 2nd restart option file
POTENTIAL ENERGY SURFACE DATA FILE
potch5j1.dat UNIT = 4
FILE NAME = potch5.dat
Polyrate 340
16.C.10. Test run ch5j1tr10
CH3 + HPh → CH4 + Ph with LCG4 calculation for all energetically accessible excited
states from a restart file in which the LCG4 calculation was
carried out for the ground state only; rate constants are also
calculated at more temperatures. (Restart file for unit fu1 is
from test run ch5j1tr5)
This sample run, like the preceding test run, is for the CH3 + HPh → CH4 + Ph reaction,
where Ph denotes a single particle with the mass of a phenyl group. The potential energy
surface and all the parameters are the same as for test run ch5j1tr5 except for the
tunneling calculations and the temperatures for which the rate constants are calculated.
In this run the tunneling calculations for ground-state transmission coefficients are
performed with the MEPSAG, CD-SCSAG, and LCG4 methods [ZCT, SCTOPT, LCTOPT].
For the LCG4 calculation, the program determines the highest excited state of the LCG4
exit arrangement which is accessible, and those excited states are included in the LCG4
calculation [ALLEXCIT].
Polyrate I/O FILES
FILE NAME Polyrate FILE NAME
ch5j1tr10.dat poly.fu5 input data file
ch5j1tr5.fu1 poly.fu1 reaction path info.
(input data for a
restart calculation)
ch5j1tr10.fu6 poly.fu6 long output file
ch5j1tr10.fu14 poly.fu14 summary output file
ch5j1tr10.fu15 poly.fu15 summary output file
POTENTIAL ENERGY SURFACE DATA FILE
potch5j1.dat UNIT = 4
FILE NAME = potch5.dat
Polyrate 341
16.C.11. Test run ch5j1tr11
CH3 + HPh → CH4 + Ph with interpolated LCG4 calculation with all energetically
accessible excited states.
This sample run for the CH3 + HPh → CH4 + Ph is similar than the previous run where
Ph denotes a single particle with the mass of a phenyl group. The only difference with
the previous test is that the large curvature tunneling energies obtained by the LCG4
method are interpolated to 9 points in the nonadiabatic zone [ILCT1D with LCTGRD
equal to 9 for all excited states]. The ILCG4 calculation includes all the final excited
states that are accessible [ALLEXCIT]. It is interesting to compare the LCG4 transmission
factors with the ones calculated in the previous run in which NGTHETA = 180.
Polyrate I/O FILES
FILE NAME Polyrate FILE NAME
ch5j1tr11.dat poly.fu5 input data file
ch5j1tr11.fu6 poly.fu6 long output file
ch5j1tr11.fu14 poly.fu14 summary output file
ch5j1tr11.fu15 poly.fu15 summary output file
POTENTIAL ENERGY SURFACE DATA FILE
potch5j1.dat UNIT = 4
FILE NAME = potch5.dat
Polyrate 342
16.C.12. Test run ch5j2tr1
CH3 + H2 → CH4 + H with harmonic approximation and ES1 method
This sample run for the reaction CH3 + H2 → CH4 + H with the J2 potential energy
surface is similar to the one described in Subsection 16.C.1. In addition to employing a
different potential energy surface, a major difference between this test run and test run
ch5j1tr1 is the method of calculating the MEP. Also, the LCG3 calculation is omitted in
this run. To calculate the MEP, a step size of 0.001 bohr is used for the first five steps
from the saddle point [SFIRST] and then a larger step size (0.01 bohr) [SSTEP] is used for
the remaining steps in combination with the Euler stabilization (ES1) method [RPM =
es1]. In addition, sixth-order Lagrangian interpolation is used to obtain the values of the
effective mass for the CD-SCSAG tunneling calculation [SCTOPT : lagrange] .
Polyrate I/O FILES
FILE NAME Polyrate FILE NAME
ch5j2tr1.dat poly.fu5 input data file
ch5j2tr1.fu6 poly.fu6 long output file
ch5j2tr1.fu14 poly.fu14 summary output file
ch5j2tr1.fu15 poly.fu15 summary output file
POTENTIAL ENERGY SURFACE DATA FILE
potch5j2.dat UNIT = 4
FILE NAME = potch5.dat
Polyrate 343
16.C.13. Test run ch5j1tr12
CH3 + HPh → CH4 + Ph with 2D interpolated LCG4 with all energetically
accessible excited states.
In this run the CH3 + HPh → CH4 + Ph thermal rate constants are calculated with the
LCT4 method with all energetically accessible vibrational excited states. As in the
previous run Ph denotes a single particle with the mass of the phenyl group. The only
difference with previous test is that both the tunneling energies and the points along each
tunneling energies are obtained from a grid specified by LCTGRD and fitted to a 2D
spline under tension [option ILCT2D in LCTOPT]. The rectangular grid was built from 7
tunneling energies and 11 points along each tunneling energy. It is interesting to compare
this run with the previous one, which uses a 1D interpolation and with test ch5j1tr10,
which corresponds to the full LCT4 calculation.
Polyrate I/O FILES
FILE NAME Polyrate FILE NAME
ch5j1tr12.dat poly.fu5 input data file
ch5j1tr12.fu6 poly.fu6 long output file
ch5j1tr12.fu14 poly.fu14 summary output file
ch5j1tr12.fu15 poly.fu15 summary output file
POTENTIAL ENERGY SURFACE DATA FILE
potch5j1 UNIT = 4
FILE NAME = potch5.dat
Polyrate 344
16.C.14. Test run ch5j2tr2
CH3 + H2 → CH4 + H with MEP only
This sample run is for the reaction CH3 + H2 → CH4 + H. The RATE and TUNNEL
sections are not given so the rate constants are not calculated. The MEP is calculated
using the ESD method [RPM = esd]. The MEP information is printed [PRINTSTEP] at grid
points separated by 0.01 bohr [SSTEP]. The overall translations and rotations are projected
out at stationary points [PROJECT].
Polyrate I/O FILES
FILE NAME Polyrate FILE NAME
ch5j2tr2.dat poly.fu5 input data file
ch5j2tr2.fu6 poly.fu6 long output file
POTENTIAL ENERGY SURFACE DATA FILE
potch5j2.dat UNIT = 4
FILE NAME = potch5.dat
Polyrate 345
16.C.15. Test run ch5j2tr3
CH3 + H2 → CH4 + H with WKB approximation for two modes
This sample run is for the reaction CH3 + H2 → CH4 + H using a combination of
methods for treating the various normal modes [VANHAR]. All reactants and products are
treated harmonically. Along the reaction path the two lowest frequency modes are
treated using the uniform WKB method with a quadratic-quartic fit to the potential at two
input distances along the generalized normal modes [QQSEMI] and the rest of the modes
are treated using the harmonic approximation. The rate constants are calculated at five
temperatures [TEMP], and four temperature pairs are used to compute activation energies
[EACT]. Both CVT [CVT] and ICVT [ICVT] rate constants are calculated, using both
MEPSAG and CD-SCSAG tunneling corrections [ZCT, SCT]. The ESD integrator [RPM =
esd] is used to calculate the MEP, using a step size of 0.001 bohr [SSTEP]. The limits
for the MEP are determined by using two keywords: SRANGE and SPECSTOP. A
generalized normal mode analysis is performed every 0.01 bohr [INH = 10].
Polyrate I/O FILES
FILE NAME Polyrate FILE NAME
ch5j2tr3.dat poly.fu5 input data file
ch5j2tr3.fu6 poly.fu6 long output file
ch5j2tr3.fu14 poly.fu14 summary output file
ch5j2tr3.fu15 poly.fu15 summary output file
POTENTIAL ENERGY SURFACE DATA FILE
potch5j2.dat UNIT = 4
FILE NAME = potch5.dat
Polyrate 346
16.C.16. Test run ch5j2itr1
CH3 + H2 → CH4 + H with zero-order IVTST approximation
This zero-order IVTST test run [IVTST0] is for the reaction CH3 + H2 → CH4 + H using
the energies, geometries, and vibrational frequencies of the reactants, saddle point, and
products from the J2 potential of Joseph et al. [Ref. 17, Sect. 21].* All reactants and
products are treated harmonically. The rate constants are calculated at four temperatures
[TEMP]. This test run reproduces the results from one of the test cases in Ref. 26 in Sect.
21.
Polyrate I/O FILES
FILE NAME Polyrate FILE NAME
ch5j2itr1.dat poly.fu5 input data file
ch5j2itr1.fu29 poly.fu29 input data file
ch5j2itr1.fu6 poly.fu6 long output file
* The data are input by means of the unit fu29 file.
Polyrate 347
16.C.17. Test run ch5j2itr2
CH3 + H2 → CH4 + H with first-order IVTST approximation
This first-order IVTST test run [IVTST1] is for the reaction CH3 + H2 → CH4 + H using
the energies, geometries, and vibrational frequencies of the reactants, saddle point,
products, and a point on the MEP at s = 0.01 bohr from the J2 potential of Joseph et al.
[Ref. 17, Sect. 21].* All reactants and products are treated harmonically. The rate
constants are calculated at four temperatures [TEMP]. This test run reproduces the results
from one of the test cases in Ref. 26 in Sect. 21.
Polyrate I/O FILES
FILE NAME Polyrate FILE NAME
ch5j2itr2.dat poly.fu5 input data file
ch5j2itr2.fu29 poly.fu29 input data file
ch5j2itr2.fu6 poly.fu6 long output file
* The data are input by means of the unit fu29 file.
Polyrate 348
16.C.18. Test run ch5fu29tr1
CH3 + H2 → CH4 + H zero-order IVTST reaction rate with electronic structure data
read from file fu29 and frequencies input directly.
This is a zero-order IVTST test run for the reaction CH3 + H2 → CH4 + H [IVTST0].
Electronic structure information calculated at the UHF/STO-3G level (energies and
frequencies) is read from unit fu29. At this level of electronic structure theory, CH3 is
nonplanar; therefore the symmetry number of the forward reaction is 2 [SIGMAF=2]. All
reactants and products are treated harmonically and the frequencies are in cm-1. The TST
rate constants [TST, NOCVT] are calculated at four temperatures [TEMP] with zero-
curvature transmission coefficients calculation. [ZCT] The zero-order IVTST calculation
can also be done with the fu50 option. A similar test run (ch5fu50tr1) can be used to
check the result.
Polyrate I/O FILES
FILE NAME Polyrate FILE NAME
ch5fu29tr1.dat poly.fu5 input data file
ch5fu29tr1.fu29 poly.fu29 input data file
ch5fu29tr1.fu6 poly.fu6 long output file
Polyrate 349
16.C.19. Test run ch5fu29tr2
CH3 + H2 → CH4 + H zero-order IVTST reaction rate with information read from fu29
and Hessian matrix input in packed form
This is a zero-order IVTST test run [TST, CVT] for the reaction CH3 + H2 → CH4 + H
[IVTST0]. Electronic structure information calculated at the UHF/STO-3G level
(Hessians of reactants, saddle point, and products in packed format) is read from file
fu29. At this level of electronic structure theory, CH3 is nonplanar; therefore the
symmetry number of the forward reaction is 2 [SIGMAF=2]. All reactants and products
are treated harmonically. Hessians and geometries are input in unscaled Cartesian
coordinates in bohrs. The rate constants are calculated at four temperatures [TEMP]. A
similar calculation has been done in the ch5tr29tr1 and ch5fu50tr1 test runs.
Polyrate I/O FILES
FILE NAME Polyrate FILE NAME
ch5fu29tr2.dat poly.fu5 input data file
ch5fu29tr2.fu29 poly.fu29 input data file
ch5fu29tr2.fu6 poly.fu6 long output file
Polyrate 350
16.C.20. Test run ch5fu30tr1
CH3 + H2 → CH4 + H TST reaction rate with frequencies read from fu30 directly
This is a conventional TST test run for the reaction CH3 + H2 → CH4 + H [NOCVT and
TST]. Electronic structure information calculated at the UHF/STO-3G level (energies and
frequencies of reactants, saddle point, and products) is read from file fu30 [POTENTIAL =
unit30]. At this level of electronic structure theory, CH3 is nonplanar; therefore the
symmetry number of the forward reaction is 2 [SIGMAF=2]. Harmonic frequencies of
reactants and products are input in atomic units [LOPT(4) = 0 in unit fu30]. The rate
constants are calculated at four temperatures [TEMP].
Polyrate I/O FILES
FILE NAME Polyrate FILE NAME
ch5fu30rt1.dat poly.fu5 input data file
ch5fu30tr1.fu30 poly.fu30 input data file
ch5fu30tr1.fu6 poly.fu6 long output file
Polyrate 351
16.C.21. Test run ch5fu30tr2
CH3 + H2 → CH4 + H TST reaction rate with information read from fu30 and full
Hessian matrices input
This is a conventional TST test run for the reaction CH3 + H2 → CH4 + H [NOCVT and
TST]. Electronic structure information calculated at the UHF/STO-3G level (energies and
full matrix format Hessians of reactants, saddle point, and products) is read from file fu30
[POTENTIAL = unit30]. At this level of electronic structure theory, CH3 is nonplanar;
therefore the symmetry number of the forward reaction is 2 [SIGMAF=2]. All reactants
and products are treated harmonically. Hessians and geometries are input in unscaled
Cartesian coordinates in atomic units [LOPT(4) = 1 and LOPT(3) = 0, respectively, in unit
fu30]. The rate constants are calculated at four temperatures [TEMP].
Polyrate I/O FILES
FILE NAME Polyrate FILE NAME
ch5fu30tr2.dat poly.fu5 input data file
ch5fu30tr2.fu30 poly.fu30 input data file
ch5fi30tr2.fu6 poly.fu6 long output file
Polyrate 352
16.C.22. Test run ch5fu30tr3
CH3 + H2 → CH4 + H TST reaction rate with information read from fu30 and Hessian
matrix input in packed form
This is a conventional TST test run for the reaction CH3 + H2 → CH4 + H [NOCVT and
TST]. Electronic structure information calculated at the UHF/STO-3G level (energies and
Hessians of reactants, saddle point, and products in packed format) is read from file fu30
[POTENTIAL = unit30]. At this level of electronic structure theory, CH3 is nonplanar;
therefore the symmetry number of the forward reaction is 2 [SIGMAF=2]. All reactants
and products are treated harmonically (some anharmonicity options are not supported for
conventional TST calculations in POLYRATE–2017). Hessians are input in unscaled
Cartesian coordinates in atomic units [LOPT(4) = -1 in unit fu30]. The rate constants are
calculated at four temperatures [TEMP].
The electronic structure information for this run was generated with the GAMESS
electronic structure package (Aug. 11, 1994 – IBM version), which yields an H2
stretching frequency of 5479.11 cm-1. POLYRATE, with this input, yields 5479.18 cm-1.
The GAUSSIAN94 electronic structure package yields a slightly different Hessian and a
frequency of 5478.64 cm-1.
Notice that the Hessian for H2 corresponds to the molecule being on the z-axis, whereas
the geometry corresponds to the molecule being on the y-axis. For calculating reactant
frequencies this does not matter, but such an inconsistency would matter along the
reaction path (see Section 9.B). It is worthwhile to point out that commonly-available
electronic structure packages may, by default, re-orient a molecule before computing its
Hessian.
Polyrate I/O FILES
FILE NAME Polyrate FILE NAME
ch5fu30tr3.dat poly.fu5 input data file
ch5fu30tr3.fu30 poly.fu30 input data file
ch5fu30tr3.fu6 poly.fu6 long output file
Polyrate 353
16.C.23. Test run ch5fu30tr4
CH3 + H2 → CH4 + H TST reaction rate with information read from fu30 and
frequencies input directly
This is a conventional TST test run for the reaction CH3 + H2 → CH4 + H [NOCVT and
TST]. Electronic structure information (energies and frequencies of the reactants, the
products, and the saddle point) at the QCISD/6-311G(d, p) level is read from file fu30
[POTENTIAL = unit30]. (The VMEP(s) has been scaled by a factor of 0.86 to be
consistent with Ref. 48 in Section 22. The scaling was done by hand; however, the
VSCALE keyword could have been used instead of hand scaling) At this level of electronic
structure theory, CH3 is planar; therefore the symmetry number of the forward reaction is
4 [SIGMAF=4]. Harmonic frequencies of reactants and products are input in atomic units
and geometries are input in unscaled Cartesian coordinates in bohrs. The rate constants
are calculated at twelve temperatures [TEMP].
Polyrate I/O FILES
FILE NAME Polyrate FILE NAME
ch5fu30tr4.dat poly.fu5 input data file
ch5fu30tr4.fu30 poly.fu30 input data file
ch5fu30tr4.fu6 poly.fu6 long output file
Polyrate 354
16.C.24. Test run ch5fu30tr5
CH3 + H2 → CH4 + H TST and CVT reaction rates with information along the reaction
path read from fu30
This is a sample run that illustrates the use of electronic structure input file data from unit
fu30 [POTENTIAL = unit30] in the calculation of rate constants for the reaction CH3 +
H2 → CH4 + H. Electronic structure information read from file fu30 (energies,
geometries, and Hessians of reactants, saddle point, products and a series of 60 points
along the reaction path) was calculated at the UHF/STO-3G level using GAMESS for
generating the reaction path (ES1 integrator, mass-weighted Cartesian coordinates, step
size = 0.005 amu1/2 a0) and GAUSSIAN94 for calculating the unscaled forces and Hessians
(run with geometry input in Cartesian coordinates and the NOSYMM keyword on) at the
generalized TST structures every 0.05 amu1/2 bohr along the reaction path. The strategy
for producing the electronic structure data was carefully selected in order to avoid the
reorientation of geometries along the reaction path though the different steps of the
process. At this level of electronic structure theory, CH3 is nonplanar; therefore the
symmetry number of the forward reaction is 2 [SIGMAF=2]. Geometries and forces are
input in unscaled Cartesian coordinates in atomic units [LOPT(3) = 100 in unit fu30].
Hessians are also input in unscaled Cartesian coordinates in bohr using the packed format
as obtained from the GAUSSIAN94 formatted checkpoint file [LOPT(4) = 99]. All normal
modes are treated harmonically and TST, CVT, and ICVT rate constants [CVT and ICVT]
are calculated at four temperatures [TEMP], using both MEPSAG and CD-SCSAG
tunneling transmission factors [ZCT, SCT]. Curvature components are calculated using the
derivative of the gradient with respect to s obtained from a quadratic fit of the gradient at
three points on the basic input grid [LOPT(6) = 2] which is also called the sparse input
grid. Note that the results obtained with this test run differ from those previously
reported in Ref. 20 in Sect. 21. Several errors were detected in Ref. 20 (see Section 24.B
in this manual for the corresponding errata).
Polyrate I/O FILES
FILE NAME Polyrate FILE NAME
ch5fu30tr5.dat poly.fu5 input data file
ch5fu30tr5.fu30 poly.fu30 input data file
ch5fu30tr5.fu6 poly.fu6 long output file
Polyrate 355
16.C.25. Test run ch5fu30tr6
CH3 + H2 → CH4 + H TST and CVT reaction rates with information along the
reaction path read from fu30. Frequencies evaluated in
redundant internal coordinates.
This is a sample run that illustrates the use of electronic structure input file data from unit
fu30 [POTENTIAL = unit30] in the calculation of rate constants for the reaction CH3 +
H2 → CH4 + H. Electronic structure information calculated at the UHF/STO-3G level
following the procedure explained in test run ch5fu30tr5 (energies, geometries, and
Hessians of reactants, products, saddle point, and a series of 50 points along the reaction
path) is read from file fu30. At this level of electronic structure theory, CH3 is
nonplanar; therefore the symmetry number of the forward reaction is 2 [SIGMAF=2].
Geometries and forces are input in unscaled Cartesian coordinates in atomic units
[LOPT(3) = 100 in unit fu30]. Hessians are also input in unscaled Cartesian coordinates in
atomic units using the packed format as obtained from the GAUSSIAN94 formatted
checkpoint file [LOPT(4) = 99]. All normal modes are treated harmonically in redundant
internal coordinates [COORD = curv3], and TST, CVT, and ICVT rate constants [CVT
and ICVT] are calculated at four temperatures [TEMP], using both MEPSAG and CD-
SCSAG tunneling transmission factors [ZCT, SCT].
The ‘Cartesian Forces’ from the GAUSSIAN94 formatted checkpoint file are actually
Cartesian Gradients; use of them as forces will introduce errors in the transformation
from rectilinear to curvilinear internal coordinates. Also, the gradients (or forces) must
be un-normalized in order to carry out the transformation correctly.
Polyrate I/O FILES
FILE NAME Polyrate FILE NAME
ch5fu30tr6.dat poly.fu5 input data file
ch5fu30tr6.fu30 poly.fu30 input data file
ch5fu30tr6.fu6 poly.fu6 long output file
Polyrate 356
16.C.26. Test run ch5fu31tr1
CH4 + H → CH3 + H2 IVTST-M-56/6 calculation using fu31
This sample run performs a IVTST-M-56/6 calculation using an fu31 input file. The
curvature components are interpolated, the vibrational analysis is carried out in redundant
internal coordinates, and ICVT rate constants are calculated. The information in the fu31
input file was obtained from the J1 potential energy surface by means of the WRITEFU31
keyword. Only the forward rate constant were calculated.
Polyrate I/O FILES
FILE NAME Polyrate FILE NAME
ch5fu31tr1.dat poly.fu5 input data file
ch5fu31tr1.fu31 poly.fu31 input data file
ch5fu31tr1.fu6 poly.fu6 long output file
ch5fu31tr1.fu15 poly.fu15 summary output file
Polyrate 357
16.C.27. Test run ch5fu40tr1
CH3 + H2 → CH4 + H TST reaction rate with frequencies read from fu40 directly
This is a conventional TST test run for the reaction CH3 + H2 → CH4 + H [NOCVT and
TST]. Electronic structure information calculated at the UHF/STO-3G level (energies,
and frequencies of reactants, saddle point, and products) is read from file fu40
[POTENTIAL = unit40]. At this level of electronic structure theory, CH3 is nonplanar;
therefore the symmetry number of the forward reaction is 2 [SIGMAF=2]. Harmonic
frequencies of reactants, products, and saddle point are input in atomic units
[FREQSOURCE = read and FREQUNIT = au in unit fu40] and geometries are input in
unscaled Cartesian coordinates in bohrs [GEOMUNIT = bohr in unit fu40]. The rate
constants are calculated at four temperatures [TEMP].
Polyrate I/O FILES
FILE NAME Polyrate FILE NAME
ch5fu40rt1.dat poly.fu5 input data file
ch5fu40tr1.fu40 poly.fu40 input data file
ch5fu40tr1.fu6 poly.fu6 long output file
Polyrate 358
16.C.28. Test run ch5fu40tr2
CH3 + H2 → CH4 + H TST reaction rate with information read from fu40 and full
Hessian matrix for frequency input
This is a conventional TST test run for the reaction CH3 + H2 → CH4 + H [NOCVT and
TST]. Electronic structure information calculated at the UHF/STO-3G level (energies and
full matrix format Hessians [HESSFORM = full ] of reactants, saddle point, and products)
is read from file fu40 [POTENTIAL = unit40]. At this level of electronic structure
theory, CH3 is nonplanar; therefore the symmetry number of the forward reaction is 2
[SIGMAF=2]. All reactants and products are treated harmonically. Hessians and
geometries are input in unscaled Cartesian coordinates in atomic units [HESSUNIT = bohr
and GEOMUNIT = bohr, respectively, in unit fu40]. The rate constants are calculated at
four temperatures [TEMP].
Polyrate I/O FILES
FILE NAME Polyrate FILE NAME
ch5fu40tr2.dat poly.fu5 input data file
ch5fu40tr2.fu40 poly.fu40 input data file
ch5fi40tr2.fu6 poly.fu6 long output file
Polyrate 359
16.C.29. Test run ch5fu40tr3
CH3 + H2 → CH4 + H TST reaction rate with information read from fu40 and Hessian
matrix input in packed form
This is a conventional TST test run for the reaction CH3 + H2 → CH4 + H [NOCVT and
TST]. Electronic structure information calculated at the UHF/STO-3G level (energies and
Hessians of reactants, saddle point, and products in packed format [HESSFORM =
packed]) is read from file fu40 [POTENTIAL = unit40]. At this level of electronic
structure theory, CH3 is nonplanar; therefore the symmetry number of the forward
reaction is 2 [SIGMAF=2]. All reactants and products are treated harmonically. Hessians
and geometries are input in unscaled Cartesian coordinates in bohrs [HESSUNIT = bohr
and GEOMUNIT = bohr, respectively, in unit fu40]. The rate constants are calculated at
four temperatures [TEMP].
Polyrate I/O FILES
FILE NAME Polyrate FILE NAME
ch5fu40tr3.dat poly.fu5 input data file
ch5fu40tr3.fu40 poly.fu40 input data file
ch5fu40tr3.fu6 poly.fu6 long output file
Polyrate 360
16.C.30. Test run ch5fu40tr4
CH3 + H2 → CH4 + H TST reaction rate with information read from fu40 and
frequencies input directly.
This is a conventional TST test run for the reaction CH3 + H2 → CH4 + H [NOCVT and
TST]. Electronic structure information (energies and frequencies of reactants, saddle
point, and products) at the QCISD/6-311G(d, p) level is read from file fu40 [POTENTIAL =
unit40]. (The VMEP(s) has been scaled by a factor of 0.86 to be consistent with Ref. 48
in Section 22. The scaling was done by hand; however, the VSCALE keyword could have
been used instead of hand scaling) At this level of electronic structure theory, CH3 is
planar; therefore the symmetry number of the forward reaction is 4 [SIGMAF=4].
Harmonic frequencies of reactants and products are input in wavenumbers [FREQSOURCE
= read, FREQUNIT = waven]. The rate constants are calculated at twelve temperatures
[TEMP].
Polyrate I/O FILES
FILE NAME Polyrate FILE NAME
ch5fu40tr4.dat poly.fu5 input data file
ch5fu40tr4.fu40 poly.fu40 input data file
ch5fu40tr4.fu6 poly.fu6 long output file
Polyrate 361
16.C.31. Test run ch5fu40tr5
CH3 + H2 → CH4 + H TST and CVT reaction rates with information along the
reaction path read from fu40
This is a sample run that illustrates the use of electronic structure input file data from unit
fu40 [POTENTIAL = unit40] in the calculation of rate constants for the reaction CH3 +
H2 → CH4 + H. Electronic structure information read from file fu40 (energies,
geometries, and Hessians of reactants, products, saddle point, and a series of 60 points
along the reaction path) was calculated at the UHF/STO-3G level using GAMESS for
generating the reaction path (ES1 integrator, mass-weighted Cartesian coordinates, step
size = 0.005 amu1/2 a0) and GAUSSIAN94 for calculating the unscaled forces and Hessians
(run with geometry input in Cartesian coordinates and the NOSYMM keyword on) at the
generalized TST structure every 0.05 amu1/2 bohr along the reaction path. The strategy
for producing the electronic structure data was carefully selected in order to avoid the
reorientation of geometries along the reaction path through the different steps of the
process. At this level of electronic structure theory, CH3 is nonplanar; therefore the
symmetry number of the forward reaction is 2 [SIGMAF=2]. Geometries and forces are
input in unscaled Cartesian coordinates in atomic units [GEOMUNIT = bohr and
GRADUNIT = bohr, respectively, in unit fu40]. Hessians are also input in unscaled
Cartesian coordinates in atomic units using the packed format as obtained from the
GAUSSIAN94 formatted checkpoint file [HESSUNIT = bohr and HESSFORM = packed].
All normal modes are treated harmonically and TST, CVT, and ICVT rate constants [CVT
and ICVT] are calculated at four temperatures [TEMP], using both MEPSAG and CD-
SCSAG tunneling transmission factors [ZCT, SCT]. Curvature components are calculated
using the derivative of the gradient with respect to s obtained from a quadratic fit of the
gradient at three points on the basic input grid [CURVATURE = compute, GRADDER =
noextra], which is also called the sparse input grid. Note that the results obtained with
this test run differ from those previously reported in Ref. 20 in Sect. 21. Several errors
were detected in Ref. 20 (see Section 24.B in this manual for the corresponding errata).
Polyrate 362
Polyrate I/O FILES
FILE NAME Polyrate FILE NAME
ch5fu40tr5.dat poly.fu5 input data file
ch5fu40tr5.fu40 poly.fu40 input data file
ch5fu40tr5.fu6 poly.fu6 long output file
Polyrate 363
16.C.32. Test run ch5fu40tr6
CH3 + H2 → CH4 + H TST and CVT reaction rates with information along the reaction
path read from fu40. Frequencies are evaluated with redundant
internal coordinates.
This is a sample run that illustrates the use of electronic structure input file data from unit
fu40 [POTENTIAL = unit40] in the calculation of rate constants for the reaction CH3 +
H2 → CH4 + H. Electronic structure information calculated at the UHF/STO-3G level
following the procedure explained in test run ch5fu40tr5 (energies, geometries, and
Hessians of reactants, saddle point, products and a series of 50 points along the reaction
path) is read from file fu40. At this level of electronic structure theory, CH3 is
nonplanar; therefore the symmetry number of the forward reaction is 2 [SIGMAF=2].
Geometries and forces are input in unscaled Cartesian coordinates in atomic units
[GEOMUNIT = bohr and GRADUNIT = bohr, respectively, in unit fu40]. Hessians are
also input in unscaled Cartesian coordinates in atomic units using the packed format as
obtained from the GAUSSIAN94 formatted checkpoint file [HESSUNIT = bohr and
HESSFORM = packed]. All normal modes are treated harmonically in redundant internal
coordinates [curv3] and TST, CVT and ICVT rate constants [CVT and ICVT] are
calculated at four temperatures [TEMP], using both MEPSAG and CD-SCSAG tunneling
transmission factors [ZCT, SCT].
The quantities labeled as “Cartesian forces” in the GAUSSIAN94 formatted checkpoint file
are actually Cartesian gradients, and using them as forces will introduce errors in the
transformation from rectilinear to curvilinear internal coordinates. Also, the gradients (or
forces) must be un-normalized in order to carry out the transformation correctly.
Polyrate I/O FILES
FILE NAME Polyrate FILE NAME
ch5fu40tr6.dat poly.fu5 input data file
ch5fu40tr6.fu40 poly.fu40 input data file
ch5fu40tr6.fu6 poly.fu6 long output file
Polyrate 364
16.C.33. Test run ch5fu50tr1
CH3 + H2 → CH4 + H zero-order IVTST reaction rate with information read from fu50
and frequencies input directly.
This is a conventional TST test run for the reaction CH3 + H2 → CH4 + H [NOCVT and
TST]. Electronic structure information calculated at the UHF/STO-3G level is read from
file fu50 [IC in unit fu5 and 0IVTST in unit fu50]. All reactants and products are treated
harmonically and the frequencies are in put in cm-1 [RCFREQA, PCFREQA, SADFREQA, and
FREQIMAG]. A rate constants are calculated at four temperatures [TEMP]. The similar
calculation can be performed with the fu29 option. Both the ch5fu29tr1 and ch5fu29tr2
test runs can be used for checking the output from different input methods.
Polyrate I/O FILES
FILE NAME Polyrate FILE NAME
ch5fu50tr1.dat poly.fu5 input data file
ch5fu50tr1.fu50 poly.fu50 input data file
ch5fu50tr1.fu6 poly.fu6 long output file
Polyrate 365
16.C.34. Test run ch5fu50tr2
CH3 + H2 → CH4 + H VTST-IOC dual-level reaction rate calculation with information
for the higher level read from fu50 and J1 analytic surface as the
lower level.
This is a VTST-IOC test run for the reaction CH3 + H2 → CH4 + H using an analytic
surface as the lower level [IC and POTENTIAL = hooks]. The potential energy is not
corrected in the nonadiabatic region in the LCT calculation [LCTCOR = nocor].
Electronic structure information calculated at the UHF/STO-3G level is read from file
fu50 and the lower-level information is obtained from the J1 surface. All the parameters
are the same as for test run ch5j1tr1.
Polyrate I/O FILES
FILE NAME Polyrate FILE NAME
ch5fu50tr2.dat poly.fu5 input data file
ch5fu50tr2.fu50 poly.fu50 input data file
ch5fu50tr2.fu6 poly.fu6 long output file
ch5fu50tr2.fu14 poly.fu14 summary output file
ch5fu50tr2.fu15 poly.fu15 summary output file
POTENTIAL ENERGY SURFACE DATA FILE
potch5j1.dat UNIT = 4
FILE NAME = potch5.dat
Polyrate 366
16.C.35. Test run ch5fu50tr3
CH3 + H2 → CH4 + H VTST-IOC dual-level reaction rate calculation with information
for the higher level read from fu50 and J1 analytic surface as the
lower level.
This is a VTST-IOC test run for the reaction CH3 + H2 → CH4 + H using an analytic
surface as the lower level [IC and POTENTIAL = hooks]. The potential energy is
corrected in the nonadiabatic region in the LCT calculation based on a quadratic
correction [LCTCOR = quadlin]. Electronic structure information calculated at the
UHF/STO-3G level is read from file fu50 and the lower-level information is obtained
from the J1 surface. All the parameters are the same as for test run ch5j1tr1.
Polyrate I/O FILES
FILE NAME Polyrate FILE NAME
ch5fu50tr3.dat poly.fu5 input data file
ch5fu50tr3.fu50 poly.fu50 input data file
ch5fu50tr3.fu6 poly.fu6 long output file
ch5fu50tr3.fu14 poly.fu14 summary output file
ch5fu50tr3.fu15 poly.fu15 summary output file
POTENTIAL ENERGY SURFACE DATA FILE
potch5j1.dat UNIT = 4
FILE NAME = potch5.dat
Polyrate 367
16.C.36. Test run ch5fu51tr1
CH3 + H2 → CH4 + H VTST-ISPE calculation with MP2/6-31G** and J1
This is a VTST-ISPE test run for the reaction CH3 + H2 → CH4 + H using an analytic
surface as the lower-level [dl and potential = hooks]. Electronic structure information
calculated at the MPS/6-31G** level is read in from file fu51 and the lower-level
information is obtained from the J1 surface. Two extra points plus the stationary points
used for the VTST-ISPE calculation were obtained from single-point energy calculations
at the MP2/6-31G** level with the configurations obtained from the lower-level surface.
All the parameters for the lower-level are the same as for the test run ch5j1tr1.
Polyrate I/O FILES
FILE NAME Polyrate FILE NAME
ch5fu51tr1.dat poly.fu5 input data file
ch5fu51tr1.fu51 poly.fu51 VTST-
ISPE input file
ch5fu51tr1.fu6 poly.fu6 long output
file
ch5fu51tr1.fu14 poly.fu14
summary output file
ch5fu51tr1.fu15 poly.fu15
summary output file
POTENTIAL ENERGY SURFACE DATA FILE
potch5j1.dat UNIT=4
FILE NAME=potch5.dat
Polyrate 368
16.C.37. Test run ch5icfu30tr1
CH3 + H2 → CH4 + H VTST-ICL-DECKART calculation using file fu30 for the lower
level information and rectilinear coordinates
This sample run uses the unit30 [POTENTIAL = unit30] and the IOC [ICOPT: icl,
deckart] options to invoke a dual-level direct dynamics calculation (variational
transition state theory with interpolated optimized corrections) on the reaction CH3 + H2
→ CH4 + H. The lower-level reaction path file is constructed at the UHF/STO-3G level,
and the higher-level interpolated optimized corrections are calculated from the
QCISD(T)/6-311G(d, p) level results. (The VMEP(s) has been scaled by a factor of 0.86 to
be consistent with Ref. 48 in Section 22. The scaling was done by hand; however, the
VSCALE keyword could have been used instead of hand scaling) All the modes are treated
harmonically. Cartesian coordinates are used [COORD = cart]. Both small-curvature
and zero-curvature tunneling calculations are carried out [ZCT, SCT]. The interpolated
optimized correction is based on the logarithm of ratios [ICOPT: icl] and an Eckart fit is
used to the energies at 3 stationary points (i.e. reactants, products, and saddle point)
[ICOPT: deckart]. At the higher level of electronic structure theory employed, CH3 is
planar; therefore the symmetry number of the forward reaction is 4 [SIGMAF=4].
Polyrate I/O FILES
FILE NAME Polyrate FILE NAME
ch5icfu30tr1.dat poly.fu5 input data file
ch5icfu30tr1.fu30 poly.fu30 input data file
ch5icfu30tr1.fu50 poly.fu50 input data file
ch5icfu30tr1.fu6 poly.fu6 output file
Polyrate 369
16.C.38. Test run ch5icfu30tr2
CH3 + H2 → CH4 + H VTST-IOC calculation using file fu30 for the lower level
information and curvilinear coordinates
This sample run uses the unit30 option [POTENTIAL = unit30] and the IOC [ICOPT:
ica, seckart] options to invoke a dual-level direct dynamics calculation with
interpolated optimized corrections on the reaction CH3 + H2 → CH4 + H. The lower-
level reaction path file is constructed at the UHF/STO-3G level, and the higher-level
interpolated optimized corrections are calculated from the QCISD(T)/6-311G(d, p) level
results. (The VMEP(s) has been scaled by a factor of 0.86 to be consistent with Ref. 48 in
Section 22. The scaling was done by hand; however, the VSCALE keyword could have
been used instead of hand scaling) The original ICA interpolated correction method is
used for the IC method. At the higher level of electronic structure theory employed, CH3
is planar; therefore the symmetry number of the forward reaction is 4 [SIGMAF = 4].
Polyrate I/O FILES
FILE NAME Polyrate FILE NAME
ch5icfu30tr2.dat poly.fu5 input data file
ch5icfu30tr2.fu30 poly.fu30 input data file
ch5icfu30tr2.fu50 poly.fu50 input data file
ch5icfu30tr2.fu6 poly.fu6 output file
Polyrate 370
16.C.39. Test run ch5icfu31tr1
CH4 + H → CH3 + H2 VTST-IOC calculation using IVTST-M-56/6 data
for the lower level of calculation and using the fu31
input file
This sample test run uses the unit31 and the IOC options to perform a dual level direct
dynamics calculation with interpolated optimized corrections. The lower level is an
IVTST-M-6/56 calculation based on the information from a fu31 input file. The higher-
level interpolated optimized corrections are calculated at the QCISD(T)/6-311G(d, p)
level with VMEP(s) scaled by a factor of 0.86, as taken from Ref. 48 in Section 22. The
ICA method is used for the correction of the frequencies, and the SECKART option is used
for the energy correction.
Polyrate I/O FILES
FILE NAME Polyrate FILE NAME
ch5fu31tr1.dat poly.fu5 input data file
ch5fu31tr1.fu31 poly.fu31 input data file
ch5fu31tr1.fu50 poly.fu50 input data file
ch5fu31tr1.fu6 poly.fu6 long output file
ch5fu31tr1.fu15 poly.fu15 summary output file
Polyrate 371
16.C.40. Test run ch5icfu40tr1
CH3 + H2 → CH4 + H VTST-ICL-DECKART calculation using file fu40 for the
lower level information and rectilinear coordinates
This sample run uses the unit40 [POTENTIAL = unit40] and the IC [ICOPT: icl,
deckart] options to invoke a dual-level direct dynamics calculation (variational
transition state theory with interpolated optimized corrections) on the reaction CH3 + H2
→ CH4 + H. The lower-level reaction path file is constructed at the UHF/STO-3G level,
and the higher-level interpolated optimized corrections are calculated from the
QCISD(T)/6-311G(d, p) level results with VMEP(s) scaled by a factor of 0.86 taken from
Ref. 48 in Section 22. All the modes are treated harmonically. Cartesian coordinates are
used [COORD = cart]. Both small-curvature and zero-curvature tunneling calculations
are carried out [ZCT, SCT]. The interpolated correction is based on the logarithm of ratios
[ICOPT: icl]. At the higher level of electronic structure theory employed, CH3 is planar;
therefore the symmetry number of the forward reaction is 4 [SIGMAF = 4].
Polyrate I/O FILES
FILE NAME Polyrate FILE NAME
ch5icfu40tr1.dat poly.fu5 input data file
ch5icfu40tr1.fu40 poly.fu40 input data file
ch5icfu40tr1.fu50 poly.fu50 input data file
ch5icfu40tr1.fu6 poly.fu6 output file
Polyrate 372
16.C.41. Test run ch5icfu40tr2
CH3 + H2 → CH4 + H VTST-IOC calculation using file fu40 for the lower level
information
This sample runuses the unit40 [POTENTIAL = unit40] and the IOC [ICOPT: ica,
seckart] options to invoke a dual-level direct dynamics calculation with interpolated
optimized corrections on the reaction CH3 + H2 → CH4 + H. The lower-level reaction
path file is constructed at the UHF/STO-3G level, and the higher-level interpolated
optimized corrections are calculated from the QCISD(T)/6-311G(d, p) level results with
VMEP(s) scaled by a factor of 0.86 taken from Ref. 48 in Section 22. The original ICA
interpolated correction procedure is used for the IOC method. At the higher level of
electronic structure theory employed, CH3 is planar; therefore the symmetry number of
the forward reaction is 4 [SIGMAF = 4].
Polyrate I/O FILES
FILE NAME Polyrate FILE NAME
ch5icfu40tr2.dat poly.fu5 input data file
ch5icfu40tr2.fu40 poly.fu40 input data file
ch5icfu40tr2.fu50 poly.fu50 input data file
ch5icfu40tr2.fu6 poly.fu6 output file
Polyrate 373
16.C.42. Test run clhbrtr1
Cl + HBr → HCl + Br with LCG3 calculations for all energetically accessible excited states in the LCG3 exit arrangement, and with the zero of energy
of the reactants determined by the program
This sample run is for the reaction Cl + HBr → HCl + Br with an extended LEPS surface.
All modes are treated using the default harmonic approximation. TST and CVT rate
constants are computed [TST, CVT]. The tunneling calculations of ground-state
transmission coefficients are performed using the MEPSAG, CD-SCSAG, and LCG3
methods [ZCT, SCT, LCTOPT]. The MEP is followed with the ESD integrator [RPM = esd]
with a step size of 0.00001 bohr [SSTEP], and a generalized normal mode analysis is
performed every 0.01 bohr [INH = 1000]. For the LCG3 calculation, the highest
energetically open vibrational state in the LCG3 exit arrangement (HCl + Br) is
determined and then all open vibrational states are included in the tunneling calculations
[ALLEXCIT] . (As always, for LCG3 calculations only the ground state is considered for
the LCG3 entrance arrangement, which is the reactant arrangement of the exoergic
direction.) Also, the theta integrals, the vibrationally adiabatic potential, the vibrational
period, and the sine of the angle between the MEP and the tunneling path at NGS0 points
between each pair of adjacent energy quadrature points are obtained by 2-point
interpolation [LCTOPT: interpolate]. This is done because the adiabatic potential of
the first vibrational excited state is not monotonic on the reactant side and, therefore,
unphysical results are obtained using interpolation with an order higher than 2. The
curvature components are calculated using a quadratic fit to obtain the derivative of the
gradient with respect to the reaction coordinate [CURV = dgrad]. The zero of energy of
the reactants is calculated from the energies of the individual molecular reactant species;
in other words, the default value of EZERO = calculate is used. Note that the
degeneracies and energies of the 2P3/2 and 2P1/2 states of Cl and Br are used in the
calculation of the reactant and product electronic partition functions. However, for the
transition state only the ground electronic state needs to be considered, because all
excited electronic states are too high in energy to have a significant effect.
The results differ from those in Ref. 10 in Sect. 21 because Ref. 10 included
anharmonicity and treated the bend in curvilinear internal coordinates, whereas the
present run is harmonic and treats all vibrations in mass-scaled Cartesians. The treatment
in Ref. 10 in Sect. 21 is more reliable.
Polyrate 374
Polyrate I/O FILES
FILE NAME Polyrate FILE NAME
clhbrtr1.dat poly.fu5 input data file
clhbrtr1.fu6 poly.fu6 long output file
clhbrtr1.fu14 poly.fu14 summary output file
clhbrtr1.fu15 poly.fu15 summary output file
Polyrate 375
16.C.43. Test run clhbrtr2
Cl + HBr → HCl + Br with LCG3 calculations in which n = 3 is the highest excited state that is included in the LCG3 exit arrangement, and with the
zero of energy of the reactants specified in the input
This sample run is similar to the clhbrtr1 test run. All vibrational modes are treated using
the default harmonic approximation. TST and CVT rate constants are computed [TST,
CVT]. The tunneling calculations of ground-state transmission coefficients are performed
using the MEPSAG, CD-SCSAG, and LCG3 methods [ZCT, SCT, LCTOPT]. For the LCG3
calculation, the n = 0, 1, 2, and 3 vibrational states in the LCG3 exit arrangement (HCl +
Br) are included in the tunneling calculation [EXCITED = 3]. The highest energetically
open vibrational state Npmax
is determined [Ref. 30 in Sect. 21], and the LCG3 tunneling
calculation includes the n = 0 to min[3, Npmax
] vibrational states in the LCG3 exit
arrangement. (For LCG3 calculations, only the ground state is considered for the LCG3
entrance arrangement, which is the reactant arrangement of the exoergic direction.) The
MEP is followed by the ESD method [RPM = esd] with a step size of 0.00001 bohr
[SSTEP] and a generalized normal mode analysis is performed every 0.01 bohr [INH =
1000]. Just as for test run clhbrtr1, we use 2-point interpolation [LCTOPT:
interpolate] for the various quantities needed in the LCG3 calculations. The
curvature components are calculated using a quadratic fit to obtain the derivative of the
gradient with respective to the reaction coordinate [CURV = dgrad]. The energy of the
reactants, which is taken as the overall zero of energy, is read from unit fu5 [EZERO =
read]. The results should be the same as those obtained in the clhbrtr1 test run.
Polyrate I/O FILES
FILE NAME Polyrate FILE NAME
clhbrtr2.dat poly.fu5 input data file
clhbrtr2.fu6 poly.fu6 long output file
clhbrtr2.fu14 poly.fu14 summary output file
clhbrtr2.fu15 poly.fu15 summary output file
Polyrate 376
16.C.44. Test run clhbrtr3
Cl + HBr → HCl + Br with LCG4 calculation for all the energetically accessible excited states in the LCG4 exit rearrangement, and with the zero of
energy determined by the program
This sample is similar to the clhbrtr1 run. All vibrational modes are treated within the
harmonic approximation. The only difference with test run clhbrtr1 is that large
curvature transmission coefficients are obtained using the LCG4 method. At each
tunneling energy a number of points along the straight path is NGTHETA = 140. The
LCG4 tunneling probabilities are evaluated at NGAMP = 40 tunneling paths.
Polyrate I/O FILES
FILE NAME Polyrate FILE NAME
clhbrtr3.dat poly.fu5 input data file
clhbrtr3.fu6 poly.fu6 long output file
clhbrtr3.fu14 poly.fu14 summary output file
clhbrtr3.fu15 poly.fu15 summary output file
Polyrate 377
16.C.45. Test run clhbrtr4
Cl + HBr → HCl + Br with interpolated LCG4 calculation for all the energetically accessible excited states in the LCG4 exit rearrangement, and
with the zero of energy determined by the program
This sample is similar to the previous clhbrtr3 test run. All vibrational modes are treated
within the harmonic approximation. The difference with the previous run is that an
interpolation is carried out, at each tunneling energy, by a splines-under-tension
procedure. In this case only 3 points were considered at each tunneling energy
[keywords ILCT and NILCGIT = 3]. Two of the three points are located at the beginning of
the nonadiabatic region and the third point is located at half the distance between the two
limiting points. This procedure still makes use of the keyword NGTHETA = 140 but the in
needed values are produced by the spline interpolation procedure. As in the previous run
the calculation takes into account all the possible open vibrational states of the exit
channel.
Polyrate I/O FILES
FILE NAME Polyrate FILE NAME
clhbrtr4.dat poly.fu5 input data file
clhbrtr4.fu6 poly.fu6 long output file
clhbrtr4.fu14 poly.fu14 summary output file
clhbrtr4.fu15 poly.fu15 summary output file
Polyrate 378
16.C.46. Test run clhbr1tr5
Cl + HBr → HCl + Br with interpolated LCG4 calculation with all the energetically
accessible excited states in the LCG4 exit rearrangement. Restart
from test run clhbrtr3.
This sample is the similar to the previous test run. The only differences are that this test
run makes use of the ILCG2D interpolation option and that a restart file is used to build
the 2D rectangular grid. In this case a quite rough grid of 5 5 is specified by LCTGRD.
Polyrate I/O FILES
FILE NAME Polyrate FILE NAME
chbrtr5.dat poly.fu5 input data file
chbrtr5.fu6 poly.fu6 long output file
chbrtr5.fu14 poly.fu14 summary output file
chbrtr5.fu15 poly.fu15 summary output file
chbrtr5.fu48 poly.fu48 LCT restart file
Polyrate 379
16.C.47. Test run cmctr1
Cl- + CH3Cl ́→ ClCH3 + Cl -́ with harmonic approximation and ES method
This sample run for the reaction Cl- + CH3Cl ́→ ClCH3 + Cl -́ uses the default harmonic
approximation for all vibrational modes. The MEP is calculated by the ESD integrator
[RPM = esd] with a step size of 0.005 bohr [SSTEP], and a generalized normal mode
analysis is performed every 0.025 bohr [INH = 5]. Both CD-SCSAG and MEPSAG
tunneling probabilities are calculated [ZCT, SCT].
This test run and the next one (cmctr2) form a pair. This one must be run before the next
one to find the s values of the wells that correspond to complexes on the reactant and
product sides of the MEP. The interpolation in test run cmctr2 on both sides of the MEP
is based on these wells, and thus we must first find the s values at these wells. A
relatively long range of the MEP (s = -7.1 bohr to s = 7.1 bohr) is calculated [SRANGE]
and we find that the s values at the wells are approximately 7.0 bohr and -7.0 bohr. We
also learn from this run that in order for the tunneling calculation to converge, the MEP
should be calculated at least from s = -1.5 bohr to s = 1.5 bohr. The saddle point
frequencies match the frequencies of the complexes in descending order (except for the
one corresponding to the reaction coordinate). We then use the information above
together with some ab initio data to make the input data file for the VTST-IOC
calculation in the cmctr2 test run.
Polyrate I/O FILES
FILE NAME Polyrate FILE NAME
cmctr1.dat poly.fu5 input data file
cmctr1.fu6 poly.fu6 long output file
cmctr1.fu14 poly.fu14 summary output file
cmctr1.fu15 poly.fu15 summary output file
POTENTIAL ENERGY SURFACE DATA FILE
potcmc1.dat UNIT = 4
FILE NAME = potcmc1.dat
potcmc2.dat UNIT = 7
FILE NAME = potcmc2.dat
Polyrate 380
16.C.48. Test run cmctr2
Cl- + CH3Cl ́→ ClCH3 + Cl -́ harmonic approximation and VTST-IOC calculation
This sample run is similar to the cmctr1 test run except we perform a VTST-IOC
calculation in addition to the VTST calculation [ICOPT] .
This reaction has two reactants and two products, but the interpolation on both sides of
the saddle point is based on wells that correspond to complexes. We set the complex
corresponding to the well on the product side to be the product so we can get its
properties, and thus we set MEPTYPER to well and MEPTYPEP to one. The correct
energy, frequency, and moment-of-inertia-tensor determinant information at reactants,
products, saddle point, and the ion-molecule complexes are obtained from the
calculations of Tucker and Truhlar [Ref. 34, Sect. 22]. The FREQMAT keyword is used,
and the frequency matching information and the s value for the ion-molecule complex are
obtained from the cmctr1 test run. The range parameters for the unit fu50 input are
obtained by the utility programs findl.f and findb.f (see Subsection 17.D) by using
additional points on the MEP that have an energy halfway between the energy of the
saddle point and the energy of reactant- or product-side stationary point.
Polyrate I/O FILES
FILE NAME Polyrate FILE NAME
cmctr2.dat poly.fu5 input data file
cmcic.dat poly.fu50 input data file
cmctr2.fu6 poly.fu6 long output file
cmctr2.fu14 poly.fu14 summary output file
cmctr2.fu15 poly.fu15 summary output file
POTENTIAL ENERGY SURFACE DATA FILE
potcmc1.dat UNIT = 4
FILE NAME = potcmc1.dat
potcmc2.dat UNIT = 7
FILE NAME = potcmc2.dat
Polyrate 381
16.C.49. Test run cmctr3
Cl- + CH3Cl ́→ ClCH3 + Cl -́ VTST-ISPE correction with MP2/6-31G**
This sample test run for the reaction Cl- + CH3Cl ́→ ClCH3 + Cl -́ uses the default
harmonic approximation for all vibrational modes. The MEP is followed by the Euler
steepest-descents integrator [ESD] with a step size of 0.005 bohr [SSTEP], and a
generalized normal mode analysis is performed every 5 gradient steps [ INH]. Both CD-
SCSAG and MEPSAG tunneling probabilities are calculated [ZCT, SCT].
This test run corrects the energies along the MEP by the VTST-ISPE method. The
energies of two extra points plus the stationary points were evaluated at the MP2/6-
31G** level with the configuration taken from the potential energy surface. The MEP is
calculated from s = -1.5 bohr to s = 1.5 bohr.
Polyrate I/O FILES
FILE NAME Polyrate FILE NAME
cmctr3.dat poly.fu5 input data file
cmctr3.fu31 poly.fu51 VTST-ISPE input file
cmctr3.fu6 poly.fu6 long output file
cmctr3.fu14 poly.fu14 summary output file
cmctr3.fu15 poly.fu15 summary output file
POTENTIAL ENERGY SURFACE DATA FILE
potcmc1.dat UNIT = 4
FILE NAME = potcmc1.dat
potcmc2.dat UNIT = 7
FILE NAME = potcmc2.dat
Polyrate 382
16.C.50. Test run cwmctr1
Cl-(H2O) + CH3Cl ́→ ClCH3 . Cl -́(H2O) TST rate constants only
In this sample run the reactant, product, and saddle point properties for the reaction Cl-
(H2O) + CH3Cl ́→ ClCH3 . Cl -́(H2O), where Cl-(H2O) represents a chloride ion in the
presence of a water molecule, are calculated, and only forward TST rate constants [TST,
FORWARDK, NOCVT] are determined. No transmission coefficients are calculated nor is
the minimum energy path determined (RATE and TUNNEL sections are not used). All
normal modes and generalized normal modes are treated using the default harmonic
approximation.
Polyrate I/O FILES
FILE NAME Polyrate FILE NAME
cwmctr1.dat poly.fu5 input data file
cwmctr1.fu6 poly.fu6 long output file
cwmctr1.fu15 poly.fu15 summary output file
POTENTIAL ENERGY SURFACE DATA FILES
potcwmc3b.dat UNIT = 4 FILE NAME = potcwmc3b.dat
potcwmcvib.dat UNIT = 7 FILE NAME =
potcwmcvib.dat
Polyrate 383
16.C.51. Test run cwmctr2
Cl-(H2O) + CH3Cl ́→ ClCH3 . Cl -́(H2O) with the hindered-internal-rotator
approximation
In this sample run for the same reaction as in the cwmctrl test run, the torsional mode of
the generalized transition state is treated with the hindered-internal-rotator
approximation [VANHAR, TOR]; all other modes are treated harmonically (default). The
ESD integrator [RPM = esd] with a step size of 0.001 bohr [SSTEP] is used to follow the
MEP, and a generalized normal mode analysis is performed every 0.01 bohr [INH = 10].
The curvature components are calculated using a quadratic fit to obtain the derivative of
the gradient with respect to the reaction coordinate [CURV = dgrad]. A restart file
containing reaction-path information is written to unit fu1 [RESTART: WRITEFU1]. Rate
constants are computed using CVT only [CVT]. The tunneling corrections are computed
using the MEPSAG and CD-SCSAG methods [ZCT, SCT]. The rate constants are
calculated for the same six temperatures as in the cwmctr1 test run [TEMP].
Polyrate I/O FILES
FILE NAME Polyrate FILE NAME
cwmctr2.dat poly.fu5 input data file
cwmctr2.fu6 poly.fu6 long output file
cwmctr2.fu1 poly.fu1 reaction path info.
cwmctr2.fu14 poly.fu14 summary output file
cwmctr2.fu15 poly.fu15 summary output file
POTENTIAL ENERGY SURFACE DATA FILES
potcwmc3b.dat UNIT = 4 FILE NAME = potcwmc3b.dat
potcwmcvib.dat UNIT = 7 FILE NAME = potcwmcvib.dat
Polyrate 384
16.C.52. Test run cwmctr3
Cl-(H2O) + CH3Cl ́→ ClCH3 . Cl -́(H2O) with the hindered-internal-rotator
approximation
In this sample run for the same reaction as in the cwmctrl test run, the torsional mode of
the generalized transition state is treated with the hindered-internal-rotator approximation
with Pitzer’s algorithm for the moment of inertia [VANHAR, TOR] and with 3=P and
31 =s ; all other modes are treated harmonically (which is the default). The ESD
integrator [RPM = esd] with a step size of 0.001 bohr [SSTEP] is used to follow the MEP,
and a generalized normal mode analysis is performed every 0.01 bohr [INH = 10]. The
curvature components are calculated using a quadratic fit to obtain the derivative of the
gradient with respect to the reaction coordinate [CURV = dgrad]. A restart file
containing reaction-path information is written to unit fu1 [RESTART: WRITEFU1]. Rate
constants are computed using CVT only [CVT]. The tunneling corrections are computed
using the MEPSAG and CD-SCSAG methods [ZCT, SCT]. The rate constants are
calculated for the same six temperatures as in the cwmctr1 test run [TEMP].
Polyrate I/O FILES
FILE NAME Polyrate FILE NAME
cwmctr3.dat poly.fu5 input data file
cwmctr3.fu6 poly.fu6 long output file
cwmctr3.fu1 poly.fu1 reaction path info.
cwmctr3.fu14 poly.fu14 summary output file
cwmctr3.fu15 poly.fu15 summary output file
POTENTIAL ENERGY SURFACE DATA FILES
potcwmc3b.dat UNIT = 4 FILE NAME = potcwmc3b.dat
potcwmcvib.dat UNIT = 7 FILE NAME = potcwmcvib.dat
Polyrate 385
16.C.53. Test run h3tr1
H2 + H ́→ HH ́+ H with WKB and Morse IIIa approximations and Page-McIver
integrator
This sample run uses the Page-McIver method [RPM = pagem] for calculating points
along the MEP of the reaction H2 + H ́→ HH ́+ H with a step size of 0.01 bohr [SSTEP] ,
evaluates the Hessian matrix and performs a generalized normal mode analysis at every
calculated point [INH = 1]. Note that the generalized transition state is restricted to linear
symmetry [SPECIES = lints]. Two different methods are used to treat the vibrational
modes [VANHAR]; vibrational modes of the reactant and product molecules and the
highest frequency mode of the generalized transition state are treated by the Morse IIIa
approximation [MORSE, MORMODEL = morseiiia], while the two lowest vibrational
modes of the generalized transition state are treated by the uniform WKB method applied
to a quadratic-quartic fit to the potential along the normal mode coordinate [QQSEMI].
Extrapolation to both reactant and product limits is performed [EXFIRST, EXSECOND].
Both CVT [CVT] and ICVT [ICVT] rate constants are calculated only in the forward
direction [FORWARDK] using both MEPSAG and CD-SCSAG tunneling corrections [ZCT,
SCT], which are computed with two equal segments in the Boltzmann and theta integrals
[NSEGBOLTZ = 2, NSEGTHETA = 2].
Polyrate I/O FILES
FILE NAME Polyrate FILE NAME
h3tr1.dat poly.fu5 input data file
h3tr1.fu6 poly.fu6 long output file
h3tr1.fu14 poly.fu14 summary output file
h3tr1.fu15 poly.fu15 summary output file
Polyrate 386
16.C.54. Test run h3tr2
H2 + H ́→ HH ́+ H with harmonic approximation and Page-McIver integrator
This sample run uses the Page-McIver method [RPM = pagem] for calculating points
along the MEP of the reaction H2 + H ́→ HH ́+ H with a step size of 0.005 bohr
[SSTEP], evaluates the Hessian matrix and performs a generalized normal mode analysis
at every 0.01 bohr [INH = 2]. The generalized transition states are restricted to linear
symmetry [SPECIES = lints]. All vibrational modes are treated by the default harmonic
approximation. Both CVT [CVT] and ICVT [ICVT] rate constants are calculated only in
the forward direction [FORWARDK], using MEPSAG, CD-SCSAG, and LCG3
transmission coefficients [ZCT, SCT, LCTOPT], in which only the ground state is included in
the LCG3 exit arrangement [NOALLEXCIT]. (We expect on physical grounds that only the
ground state needs to be considered in this case, so this option is chosen to simplify the
calculation.) The overall translations and rotations are projected out at stationary points;
this is not necessary at stationary points, but it does improve the stability of the
calculations.
Polyrate I/O FILES
FILE NAME Polyrate FILE NAME
h3tr2.dat poly.fu5 input data file
h3tr2.fu6 poly.fu6 long output file
h3tr2.fu14 poly.fu14 summary output file
h3tr2.fu15 poly.fu15 summary output file
Polyrate 387
16.C.55. Test run h3tr3
H2 + H ́→ HH ́+ H with harmonic approximation, Page-McIver integrator, and
symmetric reaction path option
This sample run is the same as test run h3tr2 except that the symmetric reaction-path
option [SYMMETRY] is used, and LCG3 transmission coefficients are not calculated, i.e.,
only MEPSAG and CD-SCSAG transmission coefficients are calculated [ZCT, SCT].
Polyrate I/O FILES
FILE NAME Polyrate FILE NAME
h3tr3.dat poly.fu5 input data file
h3tr3.fu6 poly.fu6 long output file
h3tr3.fu14 poly.fu14 summary output file
h3tr3.fu15 poly.fu15 summary output file
Polyrate 388
16.C.56. Test run h3tr4
H2 + H ́→ HH ́+ H with WKB and Morse IIIa approximations, Page-McIver
integrator, and symmetric reaction path option
This sample run is the same as test run h3tr1 except that the symmetric reaction-path
option is used [SYMMETRY].
Polyrate I/O FILES
FILE NAME Polyrate FILE NAME
h3tr4.dat poly.fu5 input data file
h3tr4.fu6 poly.fu6 long output file
h3tr4.fu14 poly.fu14 summary output file
h3tr4.fu15 poly.fu15 summary output file
Polyrate 389
16.C.57. Test run ho2tr1
OH + O → HO2 with Morse I approximation
In this sample run, CVT, VT, and US rate constants [CVT, MUVT, MUVTOPT, US] are
calculated at two temperatures [TEMP] for the reaction OH + O → HO2. (The values of
the conventional transition state theory rate constants, not computed in this sample
calculation because there is no saddle point ([STATUS = 2] in START section and
NOSADDLE in the PATH section), are set to 1.0 in the unit fu15 output.) The first step off
the starting point is followed along the negative of the gradient direction [FIRSTSTEP =
gradi]. All vibrational modes are treated by the Morse I approximation [MORSE,
MORMODEL = morsei] The MEP is followed from the input initial geometry of the
reactants by the ESD method [RPM = esd] with a step size of 0.0001 bohr [SSTEP], and a
generalized normal mode analysis is performed every 0.031 bohr [INH = 310]. Both
CD-SCSAG and MEPSAG tunneling corrections are calculated [ZCT, SCT]. Note that the
reverse rate constants are scaled by a factor of 1 15 [REVKEXP = 15]. Thirty
quadrature points were used in calculating the VT rate constants. Note that the
degeneracies and energies of the 23/2 and 21/2 states of OH and 3P2, 3P1, and 3P0 states
of O are used in the calculation of the electronic partition functions. The results may be
compared to those in Table V of Ref. 4 in Sect. 21.
Polyrate I/O FILES
FILE NAME Polyrate FILE NAME
ho2tr1.dat poly.fu5 input data file
ho2tr1.fu6 poly.fu6 long output file
ho2tr1.fu14 poly.fu14 summary output file
ho2tr1.fu15 poly.fu15 summary output file
Polyrate 390
16.C.58. Test run ho2tr2
OH + O → HO2 with Morse I approximation using curvilinear coordinates
In this sample run, CVT, VT, and US rate constants [CVT, MUVT, MUVTOPT, US] are
calculated at two temperatures [TEMP] for the reaction OH + O → HO2 using curvilinear
coordinates (O-H and O-O stretches and an H-O-O bend). (The values of the
conventional transition state theory rate constants, not computed in this sample
calculation because there is no saddle point [STATUS = 2 in START section and NOSADDLE
in the PATH section], are set to 1.0 in the unit fu15 output.) The MEP is followed from
the input initial geometry of the reactants by the ESD method [RPM = esd] with a step
size of 0.0001 bohr [SSTEP], and a generalized normal mode analysis is performed every
0.031 bohr [INH = 310]. Both CD-SCSAG and MEPSAG tunneling corrections are
calculated [ZCT, SCT]. Note that the reverse rate constants are scaled by a factor of
1 15 [REVKEXP = 15].
Polyrate I/O FILES
FILE NAME Polyrate FILE NAME
ho2tr2.dat poly.fu5 input data file
ho2tr2.fu6 poly.fu6 long output file
ho2tr2.fu14 poly.fu14 summary output file
ho2tr2.fu15 poly.fu15 summary output file
Polyrate 391
16.C.59. Test run ho2tr3
OH + O → HO2 with WKB approximation for one mode
This sample run for the reaction OH + O → HO2 uses a combination of methods for the
treatment of the vibrational modes [VANHAR]. All modes of the reactant and product
species are treated by the default harmonic approximation. The lowest frequency mode
of the generalized transition state is also treated harmonically, while the highest
frequency mode is treated by the primitive WKB method applied to a quadratic-quartic fit
of the potential along the normal mode coordinate [QQWKB]. (The values of the
conventional transition state theory rate constants, not computed in this sample
calculation because there is no saddle point [STATUS = 2 in START section and NOSADDLE
in the PATH section], are set to 1.0 in the unit fu15 output). Points along the MEP are
calculated with the ESD integrator [RPM = esd] with a step size of 0.0001 bohr [SSTEP].
A generalized normal mode analysis, together with a Hessian matrix evaluation, is
performed every 0.155 bohr [INH = 1550]. A generalized normal mode analysis is also
performed at eight special save points [SSPECIAL]. CVT [CVT] and ICVT [ICVT] rate
constants are calculated at one temperature [TEMP], using both MEPSAG and
CD-SCSAG tunneling corrections [ZCT, SCT]. Sixth-order Lagrangian interpolation is
used to obtain the values of the effective mass for CD-SCSAG tunneling [SCTOPT:
lagrange]. The reverse rate constants are scaled by a factor of 1 15 [REVEXP =
15]. Also, restart information is written to unit fu1 [RESTART: WRITEFU1].
Polyrate I/O FILES
FILE NAME Polyrate FILE NAME
ho2tr3.dat poly.fu5 input data file
ho2tr3.fu6 poly.fu6 long output file
ho2tr3.fu1 poly.fu1 reaction path info.
ho2tr3.fu14 poly.fu14 summary output file
ho2tr3.fu15 poly.fu15 summary output file
Polyrate 392
16.C.60. Test run ho2tr4
O2 + H→ HO2 with Morse I approximation
This sample run for the reaction O2 + H → HO2 uses the Morse I approximation for all
vibrational modes [MORSE, MORMODEL = morsei]. The MEP is calculated by the ESD
integrator [RPM = esd] with a step size of 0.0002 bohr [SSTEP], and a generalized normal
mode analysis is performed every 0.01 bohr [INH = 50]. Both CD-SCSAG and MEPSAG
tunneling probabilities are calculated [ZCT, SCT].
This test run forms a set with the ho2tr5 test run. Since the MEP is finite on the product
side of the saddle point and the next test run involves a VTST-IOC calculation, before
running it we must find the s value at the product. Thus, in this run we calculate a
relatively long range of the MEP (s = –2.5 bohr to s = 2.5 bohr) [SRANGE] and find that
the s value at the product is approximately 2.20 bohr. We also learn from this test run that
in order for the tunneling calculation to converge, the MEP should be calculated at least
from s = –1.8 bohr to s = 0.8 bohr. Finally we learn that the highest saddle point
frequency becomes the reactant frequency at s = –, and the second and third highest
saddle point frequencies become the product frequencies at s = 2.20 bohr. The lowest
product frequency corresponds to the reaction coordinate. We then use the information
above together with some ab initio data to make the input data file for the VTST-IOC
calculation in test run ho2tr5.
Polyrate I/O FILES
FILE NAME Polyrate FILE NAME
ho2tr4.dat poly.fu5 input data file
ho2tr4.fu6 poly.fu6 long output file
ho2tr4.fu14 poly.fu14 summary output file
ho2tr4.fu15 poly.fu15 summary output file
Polyrate 393
16.C.61. Test run ho2tr5
O2 + H→ HO2 with Morse I approximation and VTST-IOC calculation
This sample run is similar to the ho2tr4 test run except we perform a VTST-IOC
calculation in addition to the VTST calculation [ICOPT].
This reaction has two reactants and one product and a shallow well on the reactant side of
MEP. In this test run we neglect the well and set the MEPTYPER to two and MEPTYPEP to
one. The accurate energy and frequency information and the geometry for calculating
the determinant of the moment of inertia tensor at the reactants and product are obtained
from J. Chem. Phys. 74, 3482 (1981). The corrected barrier height is set to 1.0 kcal/mol
and the corrected saddle point frequencies are obtained by interpolating the correction at
reactants and product. Frequency matching information is input by the FREQMAT
keyword. We use the DETMI keyword to input the corrected determinant of the moment
of inertia tensor, and we use UNITMI to select atomic units input. The frequency-matching
information and the s value for the product are obtained from the test run ho2tr4. The
range parameters in the unit fu50 input are determined by the utility programs findl.f and
findb.f (see Subsection 17.D) by using additional points on the MEP that have energies
halfway between the energy of the saddle point and the energies of the reactant- and
product-side stationary points.
Polyrate I/O FILES
FILE NAME Polyrate FILE NAME
ho2tr5.dat poly.fu5 input data file
ho2ic.dat poly.fu50 input data file
ho2tr5.fu6 poly.fu6 long output file
ho2tr5.fu14 poly.fu14 summary output file
ho2tr5.fu15 poly.fu15 summary output file
Polyrate 394
16.C.62. Test run nh3tr1
NH3 → NH3 (inversion) with harmonic approximation and VTST-IOC calculation
This sample run is for the unimolecular reaction corresponding to the unimolecular
inversion of ammonia between two pyramidal configurations, using the default harmonic
approximation for all vibrational modes. The MEP is calculated by the ESD method
[RPM = esd] between s = 1.18 bohr and s = –1.18 bohr [SRANGE] with a step size of
0.0001 bohr [SSTEP]. A generalized normal mode analysis is performed every 0.01 bohr
[INH = 100]. MEPSAG and CD-SCSAG tunneling probabilities are calculated [ZCT,
SCT], and they can be used to study the tunneling splitting in this reaction. Rate constants
are not calculated [NOTST, NOCVT].
The VTST-IOC option is selected [ICOPT] and the accurate energy and frequency
information and the geometry for calculating the determinant of the moment of inertia
tensor are obtained from J. Chem. Phys. 93, 6570 (1990). The range parameters in the
unit fu50 input are determined by the utility programs findl.f and findb.f (see Subsection
17.D) by using additional points on the MEP that have an energy halfway between the
energy of the saddle point and the reactant/product energy.
Polyrate I/O FILES
FILE NAME Polyrate FILE NAME
nh3tr1.dat poly.fu5 input data file
nh3ic.dat poly.fu50 input data file
nh3tr1.fu6 poly.fu6 long output file
Polyrate 395
16.C.63. Test run nh3tr2
NH3 → NH3 (inversion) with harmonic approximation VTST calculation
This sample run is for the unimolecular reaction corresponding to the unimolecular
inversion of ammonia between two pyramidal configurations, using the default harmonic
approximation for all vibrational modes. The MEP is calculated by the ESD method
[RPM = esd] between s = 1.18 bohr and s = –1.18 bohr [SRANGE] with a step size of
0.0001 bohr [SSTEP]. A generalized normal mode analysis is performed every 0.01 bohr
[INH = 100]. The TST and CVT rate constants are calculated. The partition functions
and the internal free energy of reactant are printed out with PRPART = rpt. The GTLOG
keyword is used so the generalized free energy of activation is calculated using
logarithms of the individual partition functions.
This is a somewhat artificial example (because it is a degenerate rearrangement and
because ordinary pressures are too low to stabilize the system in on or another well), it is
used for testing the code.
Polyrate I/O FILES
FILE NAME Polyrate FILE NAME
nh3tr2.dat poly.fu5 input data file
nh3tr2.fu6 poly.fu6 input data file
nh3tr2.fu14 poly.fu14 summary output file
nh3tr2.fu15 poly.fu15 summary output file
Polyrate 396
16.C.64. Test run oh3tr1
OH + H2 → H2O + H with harmonic approximation and using the VRP(ESD)
algorithm
This sample run is for the OH + H2 → H2O + H reaction. The zero of energy of the
reactants is calculated from the energies of the individual molecular reactant species; in
other words, the default value of EZERO = calculate is used. All normal modes and
generalized normal modes are treated using the default harmonic approximation. The
VRP(ESD) algorithm [RPM = vrpe] with a step size of 0.001 bohr [SSTEP] is used to
follow the MEP, while the initial step from the saddle point is based on a cubic expansion
of the potential energy surface [FIRSTSTEP = cubic]. The first five steps from the saddle
point geometry in each direction are of size 0.0001 bohr [SFIRST]. The Hessian matrix is
recalculated and a generalized normal mode analysis is performed every 0.01 bohr [ INH =
10].
MEPSAG and CD-SCSAG tunneling corrections [ZCT, SCT] are computed, and both CVT
[CVT] and ICVT [ICVT] rate constants are calculated at eight temperatures [TEMP]. The
derivative of the gradient with respect to the reaction coordinate is found by a quadratic
fit [CURV = dgrad]. In addition, in this test run as well as in test runs oh3tr2–oh3tr6,
extrapolation is used for the first direction from the saddle point (i.e., toward reactants)
[EXFIRST] .
Polyrate I/O FILES
FILE NAME Polyrate FILE NAME
oh3tr1.dat poly.fu5 input data file
oh3tr1.fu6 poly.fu6 long output file
oh3tr1.fu14 poly.fu14 summary output file
oh3tr1.fu15 poly.fu15 summary output file
Polyrate 397
16.C.65. Test run oh3tr2
OH + H2 → H2O + H with Morse I-quadratic-quartic approximation
This sample run for the OH + H2 → H2O + H reaction uses the Morse I and quadratic-
quartic approximations [MORSEQQ, MORMODEL = morsei] for the normal and
generalized normal modes, i.e., modes with nonzero cubic anharmonicity are treated by
the Morse I model, while modes with zero cubic anharmonicity are approximated as
quadratic-quartic oscillators. Both the CVT [CVT] and ICVT [ICVT] methods are used.
The rate constants are calculated at twelve temperatures [TEMP] and the activation
energies are computed for three temperature pairs [EACT]. The ESD integrator [RPM =
esd] with a step size of 0.0001 bohr [SSTEP] is used to follow the MEP, and a
generalized normal mode analysis is performed every 0.01 bohr [INH = 100]. Both
MEPSAG and CD-SCSAG tunneling corrections [ZCT, SCT] are computed. Note that the
derivative of the gradient with respect to the reaction coordinate is computed by the one-
sided difference method [CURV = oneside] and the free energy of activation profile is
calculated over a different range of reaction coordinate for each temperature [GTEMP].
The results can be compared to those in Table IV of Ref. 1 in Sect. 21.
Polyrate I/O FILES
FILE NAME Polyrate FILE NAME
oh3tr2.dat poly.fu5 input data file
oh3tr2.fu6 poly.fu6 long output file
oh3tr2.fu14 poly.fu14 summary output file
oh3tr2.fu15 poly.fu15 summary output file
Polyrate 398
16.C.66. Test run oh3tr3
OH ( = 0) + H2 → H2O + H with WKB and harmonic approximations
This sample run for the OH ( = 0) + H2 → H2O + H reaction uses the WKB
approximation for the ground-state energy of all normal modes [WKB], and the default
harmonic approximation for all excited-state energies. The overall translations and
rotations are not projected out at stationary points [NOPROJECT]. The MEP is followed
with the Euler stabilization (ES1) integrator [RPM = es1], with a step size of 0.001 bohr
[SSTEP], and the initial step from the saddle point is based on a cubic expansion of the
energy surface [FIRSTSTEP = cubic]. A value different from the default value for the
stabilization criterion (magnitude of the vector difference between successive gradients)
is used; it is set equal to 0.001 [ES1OPT: diffd]. A generalized normal mode analysis is
performed every 0.02 bohr [INH = 20]. CVT [CVT] and ICVT [ICVT] rate constants are
calculated at eight temperatures [TEMP]. Both MEPSAG and CD-SCSAG tunneling
corrections are calculated [ZCT, SCTOPT], and the curvature components are found by
using a quadratic fit to obtain the derivative of the gradient with respect to the reaction
coordinate [CURV = dgrad]. Sixth-order Lagrangian interpolation is used to obtain the
values of the effective mass for the CD-SCSAG tunneling calculation [SCTOPT:
LAGRANGE].
Polyrate I/O FILES
FILE NAME Polyrate FILE NAME
oh3tr3.dat poly.fu5 input data file
oh3tr3.fu6 poly.fu6 long output file
oh3tr3.fu14 poly.fu14 summary output file
oh3tr3.fu15 poly.fu15 summary output file
Polyrate 399
16.C.67. Test run oh3tr4
Adiabatic OH ( = 0) + H2( = 1) → H2O + H with Morse I quadratic-quartic
approximation
This sample run is an example of the calculation of adiabatic state-selected rate constants
[STATE = adiab] for the reaction OH ( = 0) + H2( = 1) → H2O + H. The highest-
frequency normal mode of the generalized transition state is restricted to the first excited
state, while the second highest frequency mode is restricted to the ground state. All other
normal modes of the generalized transition state are treated thermally. For the reactants,
the stretching mode of OH is restricted to the ground state, and the stretching mode of H2
is restricted to the first excited state. Finally, for the product H2O, the highest normal
mode is restricted to the excited state, the second highest mode is restricted to the ground
state, and the lowest mode is treated thermally. The Page-McIver local-quadratic
approximation integrator [RPM = pagem] with a step size of 0.001 bohr [SSTEP] is used to
follow the MEP, the Hessian matrix is recalculated and a generalized normal mode
analysis is performed every 0.01 bohr [INH = 10]. All other options and input are the
same as for test run oh3tr2 except that only the forward rate constants are calculated
[FORWARDK].
Polyrate I/O FILES
FILE NAME Polyrate FILE NAME
oh3tr4.dat poly.fu5 input data file
oh3tr4.fu6 poly.fu6 long output file
oh3tr4.fu14 poly.fu14 summary output file
oh3tr4.fu15 poly.fu15 summary output file
Polyrate 400
16.C.68. Test run oh3tr5
Diabatic OH + H2( = 1) → H2O + H with Morse I quadratic-quartic
approximation
This sample run is an example of the calculation of diabatic state-selected rate constants
[STATE = diab] for the reaction OH + H2( = 1) → H2O + H.
The adiabatic/diabatic switch occurs at s = -0.31 bohr. For s < -0.31 bohr, the highest and
second-highest frequency normal modes of the generalized transition state are restricted
to the first excited and ground state, respectively. For s > -0.31 bohr, the highest-
frequency normal mode is restricted to the ground state, while the second-highest normal
mode is restricted to the first excited state. The lowest three normal modes of the GTS
are all treated thermally for all values of s. For the reactants, the OH stretch vibration is
restricted to the ground state, while the H2 vibration is restricted to the first excited state.
The highest and second-highest frequency normal modes of the product H2O are
restricted to the ground state and first excited state, respectively, while the lowest normal
mode is treated thermally. Other options are the same as those for test run oh3tr2, except
that only forward rate constants are calculated [FORWARDK] and the free energies are
calculated over the same range of s for all temperatures [GSPEC]. The results may be
compared to those in Table I of Ref. 3 in Sect. 21.
Polyrate I/O FILES
FILE NAME Polyrate FILE NAME
oh3tr5.dat poly.fu5 input data file
oh3tr5.fu6 poly.fu6 long output file
oh3tr5.fu14 poly.fu14 summary output file
oh3tr5.fu15 poly.fu15 summary output file
Polyrate 401
16.C.69. Test run oh3tr6
OH + H2 → H2O + H with harmonic approximation and the ES1 integrator
This sample run is for the OH + H2 → H2O + H reaction. All normal modes and
generalized normal modes are treated using the default harmonic approximation. The
ES1* integrator [RPM = es1, ES1OPT: DELTA2 = SSTEP and DIFFD = 0.01] with a step size
of 0.01 bohr [SSTEP] is used to follow the MEP, while the initial step from the saddle
point is based on a cubic expansion of the potential energy surface [FIRSTSTEP = cubic].
The Hessian matrix is recalculated and a generalized normal mode analysis is performed
every 0.01 bohr [INH = 1].
MEPSAG and CD-SCSAG tunneling corrections [ZCT, SCT] are computed, and both CVT
[CVT] and ICVT [ICVT] rate constants are calculated at eight temperatures [TEMP]. The
derivative of the gradient with respect to the reaction coordinate is found by a quadratic
fit [CURV = dgrad].
Polyrate I/O FILES
FILE NAME Polyrate FILE NAME
oh3tr6.dat poly.fu5 input data file
oh3tr6.fu6 poly.fu6 long output file
oh3tr6.fu14 poly.fu14 summary output file
oh3tr6.fu15 poly.fu15 summary output file
Polyrate 402
16.C.70. Test run oh3tr7
OH + H2 → H2O + H with MEPSAG and CD-SCSAG calculations at two temperatures
(one of the test cases in Ref. 27 in Sect. 21), WRITEFU30 option
This sample run for the OH + H2 → H2O + H reaction is taken from one of the test cases
in Ref. 27 in Sect. 21. (However, Ref. 27 used the obsolete SCSAG method whereas the
current code uses CD-SCSAG.) The MEP is calculated from s = -1.0 bohr to s = 0.3 bohr
[SRANGE] using the Page-McIver method [RPM = pagem] with the cubic starting
algorithm [FIRSTSTEP = cubic]. The gradient and save step sizes are both set to 0.062
bohr [SSTEP, INH = 1]. The CVT/MEPSAG and CVT/CD-SCSAG rate constants are
calculated [CVT, ZCT, SCT] at 200K and 300K [TEMP]. All the rate constants are within
15% of the converged values obtained in the test run oh3tr1. Also, a file is written out in
unit fu30 format as an electronic structure input file with the WRITEFU30 option. The
points are not in the required ascending order. Therefore, this generated fu30 file needs
to be reordered by the user before using the file.
Polyrate I/O FILES
FILE NAME Polyrate FILE NAME
oh3tr7.dat poly.fu5 input data file
oh3tr7.fu6 poly.fu6 long output file
oh3tr7.fu14 poly.fu14 summary output file
oh3tr7.fu15 poly.fu15 summary output file
tr7old.fu30 poly.fu30 old fu30 file
oh3tr7.fu30 poly.fu30 reordered fu30 file
Polyrate 403
16.C.71. Test run oh3tr8
OH + H2 → H2O + H with MEPSAG and CD-SCSAG calculations at two
temperatures, one of the test cases in Ref. 27 in Sect. 21, using
curvilinear internal coordinates
This sample run for the OH + H2 → H2O + H reaction is taken from one of the test cases
in Ref. 27 in Sect. 21. (However, Ref. 27 used the obsolete SCSAG method, whereas the
current code uses the CD-SCSAG method that has replaced it. Other changes are that
here curvilinear internal coordinates [COORD = curv2] are used here to calculate
bound-state vibrational frequencies and generalized normal modes, and that the run uses
SPECSTOP keyword. The curvilinear internal coordinates used for the O-H + H'-H" →
H-O-H' + H" hydrogen atom transfer reaction include the O-H, H'-H", and O-H' stretches,
the H-O-H' and H"-H'-O bends, and the H"-H'-O-H dihedral [INTDEF]. The MEP is
calculated from s = -1.0 bohr to s = 1.0 bohr [SRANGE] or until the VaG curve goes below
95% from its value at the saddle point to its value at the reactants [SPECSTOP]. The MEP
is determined using the Page-McIver method [RPM = pagem] with the cubic starting
algorithm [FIRSTSTEP = cubic]. The gradient and save step sizes are both set to 0.062
bohr [SSTEP, INH = 1]. The CVT/MEPSAG and CVT/CD-SCSAG rate constants are
calculated [CVT, ZCT, SCT] at 200K and 300K [TEMP].
Polyrate I/O FILES
FILE NAME Polyrate FILE NAME
oh3tr8.dat poly.fu5 input data file
oh3tr8.fu6 poly.fu6 long output file
oh3tr8.fu14 poly.fu14 summary output file
oh3tr8.fu15 poly.fu15 summary output file
Polyrate 404
16.C.72. Test run oh3tr9
OH + H2 → H2 + H VTST calculation including a well on the reactant side and
writing a fu31 file
This sample test run writes the fu31 input file from the information calculated using an
analytical potential energy surface. The run does not require any fu31 input file and the
resulting fu31 file is ready to be used without any change. In addition, a well that is 1.28
kcal/mol more stable than the reactants is optimized, and its frequencies are calculated.
The data is written to the fu31 file.
The vibrational analysis is carried out in curvilinear coordinates, and debugging
information on this analysis is printed out to the fu6 output file.
Polyrate I/O FILES
FILE NAME Polyrate FILE NAME
ch5fu31tr1.dat poly.fu5 input data file
ch5fu31tr1.fu31 poly.fu31 input data file
ch5fu31tr1.fu50 poly.fu50 input data file
ch5fu31tr1.fu6 poly.fu6 long output file
ch5fu31tr1.fu15 poly.fu15 summary output file
Polyrate 405
16.C.73. Test run oh3tr10
OH + H2 → H2O + H with harmonic approximation and an ESD/RODS reaction
path
This sample run uses the WRITEFU31 keyword to generate an fu31 file, and it uses the
RODS keyword to make up for deficiencies in the path. All normal modes and generalized
normal modes are treated using the default harmonic approximation. The ESD integrator
[RPM = esd] with a step size of 0.05 bohr [SSTEP] is used to follow the MEP, and the
RODS algorithm [RODS] is used to correct the energies and frequencies along the path.
The Hessian matrix is recalculated and a generalized normal mode analysis is performed
every 0.05 bohr [INH = 1].
MEPSAG tunneling corrections [ZCT] are computed, and CVT [CVT] rate constants are
calculated at eight temperatures [TEMP]. The derivative of the gradient with respect to the
reaction coordinate is found by a quadratic fit [CURV = dgrad].
Polyrate I/O FILES
FILE NAME Polyrate FILE NAME
oh3tr10.dat poly.fu5 input data file
oh3tr10.fu6 poly.fu6 long output file
oh3tr10.fu14 poly.fu14 summary output file
oh3tr10.fu15 poly.fu15 summary output file
oh3tr10.fu31 poly.fu31 input data file
Polyrate 406
16.C.74. Test run oh3fu30tr1
OH + H2 → H2O + H using electronic structure input file data from file fu30 and
curvilinear internal coordinates
This sample run demonstrates the use of electronic structure input file data in the
calculation of conventional TST rate constants [POTENTIAL = unit30] for the reaction
OH + H2 → H2O + H. Hessians are read in packed format in mass-scaled coordinates
[LOPT(4) = -2 in unit fu30 input]. Note that even though the reaction path is not required
for a conventional TST rate constant calculation, the PATH section must be included in the
unit fu5 input in order to pass to the program the value of the factor used in scaling the
coordinates [SCALEMASS in the unit fu5 input], and the data for at least two points along
the reaction path have to be input from unit fu30. The curvilinear internal coordinates
[COORD = curv2] used for the O-H + H'-H" → H-O-H' + H" hydrogen atom transfer
reaction include the O-H, H'-H", and O-H' stretches, the H-O-H' and H"-H'-O bends, and
the H"-H'-O-H dihedral [INTDEF]. All normal modes are treated harmonically
[HARMONIC in the unit fu5 input].
Polyrate I/O FILES
FILE NAME Polyrate FILE NAME
oh3fu30tr1.dat poly.fu5 input data file
oh3fu30tr1.fu30 poly.fu30 input data file
oh3fu30tr1.fu6 poly.fu6 long output file
oh3fu30tr1.fu14 poly.fu14 summary output file
oh3fu30tr1.fu15 poly.fu15 summary output file
Polyrate 407
16.C.75. Test run oh3fu30tr2
OH + H2 → H2O + H using electronic structure input file data from file fu30 and
curvilinear internal coordinates
This sample run demonstrates the use of electronic structure input file data in the
calculation of rate constants [POTENTIAL = unit30] for the reaction OH + H2 → H2O +
H. This type of calculation requires the unit fu30 input file. The normal mode and
generalized normal mode frequencies are obtained at each save point on the MEP by first
transforming the Cartesian Hessian matrix into curvilinear internal coordinate space,
projecting out the gradient direction, and then diagonalizing the projected Hessian using
the Wilson GF method. The curvilinear internal coordinates [COORD = curv2] used for
the O-H + H'-H" → H-O-H' + H" hydrogen atom transfer reaction include the O-H,
H'-H", and O-H' stretches, the H-O-H' and H"-H'-O bends, and the H"-H'-O-H dihedral
[INTDEF]. The curvature components are computed using a quadratic fit to obtain the
derivative of the gradient with respect to the reaction coordinate [LOPT(6) = 4]. All
normal modes and generalized normal modes are treated harmonically [HARMONIC in the
unit fu5 input], and only TST and CVT rate constants are calculated [CVT] at four
temperatures [TEMP], using both MEPSAG and CD-SCSAG tunneling corrections [ZCT,
SCT].
Polyrate I/O FILES
FILE NAME Polyrate FILE NAME
oh3fu30tr2.dat poly.fu5 input data file
oh3fu30tr2.fu30 poly.fu30 electronic structure
input file data
oh3fu30tr2.fu6 poly.fu6 long output file
oh3fu30tr2.fu14 poly.fu14 summary output file
oh3fu30tr2.fu15 poly.fu15 summary output file
Polyrate 408
16.C.76. Test run oh3fu30tr3
OH + H2 → H2O + H direct dynamics calculation using the electronic structure data
read from file fu30, rectilinear coordinates, and IVTST-M-4/4
interpolation.
This sample run demonstrates the use of electronic structure input file data read from unit
fu30 in the calculation of rate constants [POTENTIAL = unit30] for the reaction OH +
H2 → H2O + H. This type of calculation requires the unit fu30 input file. The
interpolation is done using IVTST-M-4/4 [LOPT(2) = 500]. Note that the normal mode
and generalized normal mode frequencies are obtained by diagonalization of the matrix
of the second derivatives of the potential with respect to the mass-scaled Cartesian
coordinates, which is read in packed form from unit fu30 [LOPT(4) = -2 in the unit fu30
input], and no anharmonic data are included [LOPT(5) = 0]. All normal modes are treated
harmonically [HARMONIC in the unit fu5 input], and only TST and CVT rate constants are
calculated [CVT] at four temperatures [TEMP], using both MEPSAG and CD-SCSAG
tunneling corrections [ZCT, SCT].
Polyrate I/O FILES
FILE NAME Polyrate FILE NAME
oh3fu30tr3.dat poly.fu5 input data file
oh3fu30tr3.fu30 poly.fu30 input data file
oh3fu30tr3.fu6 poly.fu6 long output file
oh3fu30tr3.fu14 poly.fu14 summary output file
oh3fu30tr3.fu15 poly.fu15 summary output file
Polyrate 409
16.C.77. Test run oh3fu30tr4
OH + H2 → H2O + H using electronic structure input file data from file fu30 for
generating the next point along the reaction path (reactants
valley).
This sample run demonstrates the use of the NEXTPT keyword for generating the next
point along the reaction path in conjunction with the use of electronic structure input
from file fu30 [POTENTIAL = unit30] for the reaction OH + H2 → H2O + H. Note that
the print option LOPT(1) and IFITV are set equal to 0 in file fu30 because nonzero values
for these variables are incompatible with NEXTPT. Electronic structure information is
included for two points on the reaction path (one on each side of the saddle point), with
the first one having a positive s and the second one having a negative s (thus the points
are not in increasing order of s, but this is permitted when NEXTPT is on). Since the last
point has a negative s, IDIRECT is set equal to -1. The next point is generated on the
reactants side using a step size of 0.0005 amu1/2 bohr [SSTEP].
Polyrate I/O FILES
FILE NAME Polyrate FILE NAME
oh3fu30tr4.dat poly.fu5 input data file
oh3fu30tr4.fu30 poly.fu30 input data file
oh3fu30tr4.fu6 poly.fu6 long output file
Polyrate 410
16.C.78. Test run oh3fu30tr5
OH + H2 → H2O + H using electronic structure input file data from file fu30 for
generating the next point along the reaction path (products
valley).
This sample run demonstrates the use of the NEXTPT keyword for generating the next
point along the reaction path in conjunction with the use of electronic structure input
from file fu30 [POTENTIAL = unit30] for the reaction OH + H2 → H2O + H. Note that
the print option LOPT(1) and IFITV are set equal to 0 in file fu30 because nonzero values
for these variables are incompatible with NEXTPT. Electronic structure information is
included for two points on the reaction path (one on each side of the saddle point), with
the last one being in the products valley. Since the last point has a positive s, IDIRECT is
+1. The next point is generated on the products side using a step size of 0.0005 amu1/2
bohr [SSTEP].
Polyrate I/O FILES
FILE NAME Polyrate FILE NAME
oh3fu30tr5.dat poly.fu5 input data file
oh3fu30tr5.fu30 poly.fu30 input data file
oh3fu30tr5.fu6 poly.fu6 long output file
Polyrate 411
16.C.79. Test run oh3fu30tr6
OH + H2 → H2 + H fu30 calculation including a well on the reactant side
The oh3fu30tr6 test run is a sample run that uses file fu30 and includes a well on the
reactant side in the calculation. The reaction path is interpolated by means of third order
Lagrangian interpolation using the points along the reaction path including the reactant
well. The file fu30 was created with the writefu30 option, with only two changes being
necessary: to input of the value of the reaction coordinate, s, at the reactants well, and to
reorder of the points.
Polyrate I/O FILES
FILE NAME Polyrate FILE NAME
oh3fu30tr6.dat poly.fu5 input data file
oh3fu30tr6.fu30 poly.fu30 input data file
oh3fu30tr6.fu6 poly.fu6 long output file
oh3fu30tr6.fu14 poly.fu14 summary output file
oh3fu30tr6.fu15 poly.fu15 summary output file
Polyrate 412
16.C.80. Test run oh3fu31tr1
OH + H2 → H2 + H IVTST-M calculation including a well on the reactant side
This sample test run uses the unit31 option to perform an IVTST-M calculation
including a well on the reactant side. This is an IVTST-M-100/2002 calculation based on
an fu31 input file identical to the one written in the oh3tr9 test run. The value for the
step-size SINCW is set to 0.001 bohr, which is the step-size used in the generation of the
fu31 file.
Note that this run cannot be done without interpolating to the well, since the energies
given in the fu31 input file for some of the points on the reactant side are below the
energy of the infinitely separated reactants. Since the interpolation to two separated
products is based on a Eckart potential, which does not allow the presence of wells, the
algorithm would fail. Thus, the well is required in the present IVTST-M calculation. If
the information given on the reactant side of the reaction path were to be reduced to the
point where no energy lower than the reactant energy appears in the fu31 file, the
interpolation could be carried out using the reactant information.
The calculated reaction path is extended up to s = –1.70 a0 (using a scaling mass of
1.802023 a.u.). Since the well is estimated to be located at s = –1.73 a0, extending the
range of values of s further toward reactants could cause numerical errors, since the
reaction path has not been interpolated beyond the well. In general, whenever a finite
range of s is used in a IVTST-M calculation (i.e., reactions with only one reactant or only
one product, or reactions with wells), the user should check that the range of s given in
the fu5 file does not goes beyond the values of s estimated for the stationary point (or
points).
Polyrate I/O FILES
FILE NAME Polyrate FILE NAME
oh3fu31tr1.dat poly.fu5 input data file
oh3fu31tr1.fu31 poly.fu31 input data file
oh3fu31tr1.fu6 poly.fu6 long output file
oh3fu31tr1.fu15 poly.fu15 summary output file
Polyrate 413
16.C.81. Test run oh3fu31tr2
OH + DH → HOD + H direct dynamics calculation of an isotopically substituted
reaction using electronic structure data for the isotopically
unsubstituted reaction read from file fu31, using
ESD(H)/RODS, and using IVTST-M.
This sample run demonstrates how to use the OH + H2 → H2O + H reaction path along
with the ESD(H)/RODS [RODS] and IVTST-M algorithms and file fu31 [POTENTIAL =
unit31] to obtain the conventional TST, CVT, CVT/ZCT, and CVT/SCT rate constants
for the isotopically substituted reaction OH + DH → HOD + H. The ESD(H)/RODS
method is described in Ref. 50 in Sect. 21. The fu31 input file used in this run was
written using the WRITEFU31 option in a run on OH + H2 (not included in the test suite).
The KIES option must be included in the GENERAL section of file fu31 so that the correct
value of s is calculated for the isotopically substituted reaction.
Polyrate I/O FILES
FILE NAME Polyrate FILE NAME
oh3fu31tr2.dat poly.fu5 input data file
oh3fu31tr2.fu31 poly.fu31 input data file
oh3fu31tr2.fu6 poly.fu6 long output file
oh3fu31tr2.fu14 poly.fu14 summary output file
oh3fu31tr2.fu15 poly.fu15 summary output file
Polyrate 414
16.C.82. Test run oh3fu40tr1
OH + H2 → H2O + H using electronic structure input file data from file fu40 and
curvilinear internal coordinates
This sample run demonstrates the use of electronic structure input file data in the
calculation of conventional TST rate constants [POTENTIAL = unit40] for the reaction
OH + H2 → H2O + H. Hessians are read in mass-scaled coordinates [HESSFORM =
msbohr, HESSUNIT = msbohr in file fu40]. Note that even though the reaction path is
not required for a conventional TST rate constant calculation, the PATH section must be
included in the unit fu5 input in order to pass to the program the value of the factor used
in scaling the coordinates [SCALEMASS in the unit fu5 input] and at least two points along
the reaction path have to be input from unit fu40. The curvilinear internal coordinates
[COORD = curv2] used for the O-H + H'-H" → H-O-H' + H" hydrogen atom transfer
reaction include the O-H, H'-H", and O-H' stretches, the H-O-H' and H"-H'-O bends, and
the H"-H'-O-H dihedral [INTDEF]. All normal modes are treated harmonically
[HARMONIC in the unit fu5 input].
Polyrate I/O FILES
FILE NAME Polyrate FILE NAME
oh3fu40tr1.dat poly.fu5 input data file
oh3fu40tr1.fu40 poly.fu40 input data file
oh3fu40tr1.fu6 poly.fu6 long output file
oh3fu40tr1.fu14 poly.fu14 summary output file
oh3fu40tr1.fu15 poly.fu15 summary output file
Polyrate 415
16.C.83. Test run oh3fu40tr2
OH + H2 → H2O + H using electronic structure input file data from file fu40 and
curvilinear internal coordinates
This sample run demonstrates the use of electronic structure input file data in the
calculation of rate constants [POTENTIAL = unit40] for the reaction OH + H2 → H2O +
H. This type of calculation requires the unit fu40 input file. The normal mode and
generalized normal mode frequencies are obtained at each save point on the MEP by first
transforming the Cartesian Hessian matrix into curvilinear internal coordinate space,
projecting out the gradient direction, and then diagonalizing the projected Hessian using
the Wilson GF method. The curvilinear internal coordinates [COORD = curv2] used for
the O-H + H'-H" → H-O-H' + H" hydrogen atom transfer reaction include the O-H,
H'-H", and O-H' stretches, the H-O-H' and H"-H'-O bends, and the H"-H'-O-H dihedral
[INTDEF]. The curvature components are computed using a quadratic fit to obtain the
derivative of the gradient with respect to the reaction coordinate [CURVATURE =
compute and GRADDER = noextra in the unit fu40 input]. All normal modes and
generalized normal modes are treated harmonically [HARMONIC in the unit fu5 input], and
only TST and CVT rate constants are calculated [CVT] at four temperatures [TEMP], using
both MEPSAG and CD-SCSAG tunneling corrections [ZCT, SCT].
Polyrate I/O FILES
FILE NAME Polyrate FILE NAME
oh3fu40tr2.dat poly.fu5 input data file
oh3fu40tr2.fu40 poly.fu40 input data file
oh3fu40tr2.fu6 poly.fu6 long output file
oh3fu40tr2.fu14 poly.fu14 summary output file
oh3fu40tr2.fu15 poly.fu15 summary output file
Polyrate 416
16.C.84. Test run oh3fu40tr3
OH + H2 → H2O + H direct dynamics calculation using the electronic structure data
read from file fu40, using rectilinear coordinates, and IVTST-M-
4/4.
This sample run demonstrates the use of electronic structure input file data read from unit
fu40 in the calculation of rate constants [POTENTIAL = unit40] for the reaction OH +
H2 → H2O + H. This type of calculation requires the unit fu40 input file. The
interpolation is calculated using IVTST-M-4/4 [MAXLPTS = 500]. Note that the normal
mode and generalized normal mode frequencies are obtained by diagonalization of the
matrix of the second derivatives of the potential with respect to the mass-scaled Cartesian
coordinates, which is read in packed form from unit fu40 [HESSFORM = packed,
HESSUNIT = msbohr], and no anharmonic data are included [ANHARM = none]. The
curvature components are computed using a quadratic fit to obtain the derivative of the
gradient with respect to the reaction coordinate [CURVATURE = compute, GRADDER =
noextra]. All normal modes are treated harmonically [HARMONIC in the unit fu5
input], and only TST and CVT rate constants are calculated [CVT] at four temperatures
[TEMP], using both MEPSAG and CD-SCSAG tunneling corrections [ZCT, SCT].
Polyrate I/O FILES
FILE NAME Polyrate FILE NAME
oh3fu40tr3.dat poly.fu5 input data file
oh3fu40tr3.fu40 poly.fu40 input data file
oh3fu40tr3.fu6 poly.fu6 long output file
oh3fu40tr3.fu14 poly.fu14 summary output file
oh3fu40tr3.fu15 poly.fu15 summary output file
Polyrate 417
16.C.85. Test run oh3fu40tr4
OH + H2 → H2O + H using electronic structure input file data from file fu40 for
generating the next point along the reaction path (reactants
valley).
This sample run demonstrates the use of the NEXTPT keyword for generating the next
point along the reaction path in conjunction with the use of electronic structure input
from file fu40 [POTENTIAL = unit40] for the reaction OH + H2 → H2O + H. Electronic
structure information is included for two points on the reaction path (one on each side of
the saddle point), with the first one having a positive s and the second one having a
negative s (thus the points are not in increasing order of s, but this is permitted when
NEXTPT is on). Since the last point has a negative s, IDIRECT is set equal to -1. The next
point is generated on the reactants side using a step size of 0.0005 amu1/2 bohr [SSTEP].
Polyrate I/O FILES
FILE NAME Polyrate FILE NAME
oh3fu40tr4.dat poly.fu5 input data file
oh3fu40tr4.fu40 poly.fu40 input data file
oh3fu40tr4.fu6 poly.fu6 long output file
Polyrate 418
16.C.86. Test run oh3fu40tr5
OH + H2 → H2O + H using electronic structure input file data from file fu40 for
generating the next point along the reaction path (products
valley)
This sample run demonstrates the use of the NEXTPT keyword for generating the next
point along the reaction path in conjunction with the use of electronic structure input
from file fu40 [POTENTIAL = unit40] for the reaction OH + H2 → H2O + H. Electronic
structure information is included for two points on the reaction path (one on each side of
the saddle point), with the last one being in the products valley. Since the last point has a
positive s, IDIRECT is +1. The next point is generated on the products side using a step
size of 0.0005 amu1/2 bohr [SSTEP].
Polyrate I/O FILES
FILE NAME Polyrate FILE NAME
oh3fu40tr5.dat poly.fu5 input data file
oh3fu40tr5.fu40 poly.fu40 input data file
oh3fu40tr5.fu6 poly.fu6 long output file
Polyrate 419
16.C.87. Test run oh3fu40tr6
OH + H2 → H2 + H fu40 calculation including a well on the reactant side
The oh3fu40tr6 test run is a sample run that uses file fu40 and includes as the left-hand
edge of the interpolation interval a well on the reactant side in the calculation. The
reaction path is interpolated by means of third order Lagrangian interpolation using the
points along the reaction path including the reactants well.
Polyrate I/O FILES
FILE NAME Polyrate FILE NAME
oh3fu40tr6.dat poly.fu5 input data file
oh3fu40tr6.fu40 poly.fu40 input data file
oh3fu40tr6.fu6 poly.fu6 long output file
oh3fu40tr6.fu14 poly.fu14 summary output file
oh3fu40tr6.fu15 poly.fu15 summary output file
Polyrate 420
16.C.88. Test run hnitr1
H(a)/Ni(100) → H(a)/Ni(100) with harmonic approximation and ESD integrator
This sample run is for the surface diffusion reaction H(a)/Ni(100) → H(a)/Ni(100), where
both reactant and product are adsorbed species [PHASE = solid] on a fixed Ni lattice. In
this particular calculation none of the Ni atoms are allowed to move. All vibrational
modes are treated by the default harmonic approximation. Points along the MEP are
calculated by the Euler steepest-descents (ESD) integrator [RPM = esd] with a step size
of 0.0001 bohr [SSTEP], and a generalized normal mode analysis is performed every 0.02
bohr [INH = 200]. CVT rate constants [CVT] are calculated. In addition, MEPSAG and
CD-SCSAG transmission coefficients are included [ZCT, SCT]. The reaction path
curvature components are calculated using a quadratic fit to obtain the derivative of the
gradient with respect to the reaction coordinate [CURV = dgrad]. Note that the
electronic partition functions of the transition state and of the reactant are assumed to
cancel.
Polyrate I/O FILES
FILE NAME Polyrate FILE NAME
hnitr1.dat poly.fu5 input data file
hnitr1.fu6 poly.fu6 long output file
hnitr1.fu14 poly.fu14 summary output file
hnitr1.fu15 poly.fu15 summary output file
POTENTIAL ENERGY SURFACE DATA FILE
pothni.dat UNIT = 4
FILE NAME = pothni.dat
Polyrate 421
16.C.89. Test run h2nitr1
H2(a)/Ni(100) → 2H(a)/Ni(100) with harmonic approximation and ESD integrator
This sample run is for the unimolecular gas-solid-interface reaction H2(a)/Ni(100) →
2H(a)/Ni(100) where both reactant and products are adsorbed species [PHASE = solid] on
a fixed Ni lattice consisting of 817 Ni atoms. All vibrational modes are treated by the
default harmonic approximation. Points along the MEP are calculated by the ESD
integrator [RPM = esd] with a step size of 0.001 bohr [SSTEP], and a generalized normal
mode analysis is performed every 0.01 bohr [INH = 10]. CVT rate constants are
calculated [CVT] at 8 temperatures [TEMP]. In addition, MEPSAG, CD-SCSAG, and
LCG3 transmission coefficients are included [ZCT, SCT, LCTOPT], and only the ground
state is involved in the LCG3 exit arrangement for the LCG3 tunneling calculation
[NOALLEXCIT].
Polyrate I/O FILES
FILE NAME Polyrate FILE NAME
h2nitr1.dat poly.fu5 input data file
h2nitr1.fu6 poly.fu6 long output file
h2nitr1.fu14 poly.fu14 summary output file
h2nitr1.fu15 poly.fu15 summary output file
POTENTIAL ENERGY SURFACE DATA FILES
poth2niads.dat UNIT = 4 FILE NAME = poth2niads.dat
poth2nilat.dat UNIT = 7 FILE NAME = poth2nilat.dat
Polyrate 422
16.C.90. Test run ch4ohtr1
OH + CH4 → H2O + CH3 zero-order IVTST calculation
This sample run uses the ICOPT keyword [ICOPT: zero] for a zero-order IVTST (i.e.,
IVTST-0) calculation of the reaction OH + CH4 → H2O + CH3 at 19 temperatures
[TEMP]. The classical potential energy curve and the adiabatic ground-state energy curve
are approximated by Eckart functions from s = –2.0 bohr to s = 2.0 bohr [SRANGE]. The
Hessian grid spacing is set to 0.02 bohr [INH = 20]. The ab initio data taken from J.
Chem. Phys. 99, 1013 (1993) are input by means of the unit fu50 file. The ZCT keyword
is used since MEPSAG is the only semiclassical tunneling method available for the zero-
order IVTST calculation. The lowest-frequency vibrational mode of the generalized
transition state is treated as a hindered rotor [VANHAR, TOR], while all of the other modes
are treated by the default harmonic approximation.
Polyrate I/O FILES
FILE NAME Polyrate FILE NAME
ch4ohtr1.dat poly.fu5 input data file
ch4ohic.dat poly.fu50 input data file
ch4ohtr1.fu6 poly.fu6 long output file
ch4ohtr1.fu14 poly.fu14 summary output file
ch4ohtr1.fu15 poly.fu15 summary output file
Polyrate 423
16.C.91. Test run ch4ohtr2
OH + CH4 → H2O + CH3 zero-order IVTST calculation
This sample run uses the IVTST0 keyword for a zero-order IVTST (i.e., IVTST-0)
calculation of the reaction OH + CH4 → H2O + CH3 at 19 temperatures [TEMP]. The
classical potential energy curve and the adiabatic ground-state energy curve are
approximated by Eckart functions from s = -2.0 bohr to s = 2.0 bohr [SRANGE]. The
Hessian grid spacing is set to 0.02 bohr [INH = 20]. The ab initio data taken from J.
Chem. Phys. 99, 1013 (1993) are input by means of the unit fu29 file. The MEPSAG
method [ZCT] is the only semiclassical tunneling method available for the zero-order
IVTST calculation. All vibrational modes are treated by the default harmonic
approximation.
Polyrate I/O FILES
FILE NAME Polyrate FILE NAME
ch4ohtr2.dat poly.fu5 input data file
ch4ohtr2.fu29 poly.fu29 input data file
ch4ohtr1.fu6 poly.fu6 output file
Polyrate 424
16.C.92. Test run ch4ohtr3
OH + CH4 → H2O + CH3 zero-order IVTST calculation
This sample run uses the ICOPT keyword [ICOPT: zero] for a zero-order IVTST (i.e.,
IVTST-0) calculation of the reaction OH + CH4 → H2O + CH3 at 19 temperatures
[TEMP]. The classical potential energy curve and the adiabatic ground-state energy curve
are approximated by Eckart functions from s = –2.0 bohr to s = 2.0 bohr [SRANGE]. The
Hessian grid spacing is set to 0.02 bohr [INH = 20]. The ab initio data taken from J.
Chem. Phys. 99, 1013 (1993) are input by means of the unit fu50 file. The ZCT keyword
is used since MEPSAG is the only semiclassical tunneling method available for the zero-
order IVTST calculation. This sample run is the same as the ch4ohtr1 test run, except
that the lowest-frequency vibrational mode of the generalized transition state is treated as
a hindered rotor using the CO torsion option.
Polyrate I/O FILES
FILE NAME Polyrate FILE NAME
ch4ohtr3.dat poly.fu5 input data file
ch4ohic.dat poly.fu50 input data file
ch4ohtr3.fu6 poly.fu6 long output file
ch4ohtr3.fu14 poly.fu14 summary output file
ch4ohtr3.fu15 poly.fu15 summary output file
Polyrate 425
16.C.93. Test run ch4ohtr4
OH + CH4 → H2O + CH3 zero-order IVTST calculation
This sample run uses the ICOPT keyword [ICOPT: zero] for a zero-order IVTST (i.e.,
IVTST-0) calculation of the reaction OH + CH4 → H2O + CH3 at 19 temperatures
[TEMP]. The classical potential energy curve and the adiabatic ground-state energy curve
are approximated by Eckart functions from s = –2.0 bohr to s = 2.0 bohr [SRANGE]. The
Hessian grid spacing is set to 0.02 bohr [INH = 20]. The ab initio data taken from J.
Chem. Phys. 99, 1013 (1993) are input by means of the unit fu50 file. The ZCT keyword
is used since MEPSAG is the only semiclassical tunneling method available for the zero-
order IVTST calculation. This sample run is the same as the ch4ohtr1 test run, except that
the lowest-frequency vibrational mode of the generalized transition state is treated as a
hindered rotor using the CW torsion option.
Polyrate I/O FILES
FILE NAME Polyrate FILE NAME
ch4ohtr4.dat poly.fu5 input data file
ch4ohic.dat poly.fu50 input data file
ch4ohtr4.fu6 poly.fu6 long output file
ch4ohtr4.fu14 poly.fu14 summary output file
ch4ohtr4.fu15 poly.fu15 summary output file
Polyrate 426
16.C.94. Test run ch4cltr1
CH4 + Cl → HCl + CH3 zero-order IVTST calculation
This sample run uses the IVTST0 keyword for a zero-order IVTST (i.e., IVTST-0)
calculation of the reaction CH4 + Cl → HCl + CH3 at 4 temperatures [TEMP]. The
classical potential energy curve and the adiabatic ground-state energy curve are
approximated by Eckart functions from s = -1.0 bohr to s = 1.5 bohr [SRANGE]. The
Hessian grid spacing is set to 0.02 bohr [INH = 4]. The ab initio data are input by means
of the unit fu29 file. The MEPSAG method is the only semiclassical tunneling method
available for the zero-order IVTST calculation. All vibrational modes are treated by the
default harmonic approximation. The 2P3/2 and 3P1/2 states of Cl are used in the
calculation of the electronic partition functions [ELEC]. [This test run reproduces the
results of one of the test cases in Ref. 26 in Sect. 21.]
Polyrate I/O FILES
FILE NAME Polyrate FILE NAME
ch4cltr1.dat poly.fu5 input data file
ch4cltr1.fu29 poly.fu29 input data file
ch4cltr1.fu6 poly.fu6 output file
Polyrate 427
16.C.95. Test run ch4cltr2
CH4 + Cl → HCl + CH3 first-order IVTST calculation
This sample run uses the IVTST1 keyword for a first-order IVTST (i.e., IVTST-1)
calculation of the reaction CH4 + Cl → HCl + CH3 at 4 temperatures [TEMP]. The
classical potential energy curve and the adiabatic ground-state energy curve are
approximated by Eckart functions from s = –1.0 bohr to s = 1.5 bohr [SRANGE]. The
Hessian grid spacing is set to 0.02 bohr [INH = 4]. The ab initio data are input by means
of the unit fu29 file. Both MEPSAG and SCSAG semiclassical tunneling methods [ZCT,
SCT] are used, since they are available for the first-order IVTST calculation. All
vibrational modes are treated by the default harmonic approximation. The 2P3/2 and 3P1/2
states of Cl are used in the calculation of the electronic partition functions[ELEC]. [This
test run reproduces the results of one of the test cases in Ref. 26 in Sect. 21.]
Polyrate I/O FILES
FILE NAME Polyrate FILE NAME
ch4cltr2.dat poly.fu5 input data file
ch4cltr2.fu29 poly.fu29 input data file
ch4cltr2.fu6 poly.fu6 output file
Polyrate 428
16.C.96. Test run ch4otr1
CH4 + O → CH3 + OH CUS calculation using harmonic redundant curvilinear
coordinates
This sample run calculates canonical unified statistical model (CUS) rate constants
including MEPSAG, CD-SCSAG, LCG3, COMT, and OMT tunneling, based on the
information from an analytical potential energy surface. The reaction has two different
electronic states, but since they are very close in energy, they are assumed to be
represented by the same surface. Thus, the total rate constant should be multiplied by a
factor of 2 in order to take into account this electronic degeneracy. This is done by using
a factor of 6 for the saddle point electronic degeneracy instead of its value of 3.
The VaG(s) curve has two maxima near the saddle point. In order to estimate the
recrossing effects due to these maxima a CUS calculation is performed.
Polyrate I/O FILES
FILE NAME Polyrate FILE NAME
ch4otr1.dat poly.fu5 input data file
ch4otr1.fu6 poly.fu6 long output file
ch4otr1.fu14 poly.fu14 summary output file
ch4otr1.fu15 poly.fu15 summary output file
POTENTIAL ENERGY SURFACE DATA FILE
potch4o.dat UNIT = 4
FILE NAME = potch4o.dat
Polyrate 429
16.C.97. Test run ohcltr1
O + HCl → OH + Cl ICVT calculation using Morse 1 anharmonicity and internal
coordinates
This sample run calculates improved canonical variational theory (ICVT) rate constants
including MEPSAG and CD-SCSAG tunneling, based on the information from an
analytical potential energy surface. The saddle point and generalized transition states are
nonlinear [SPECIES = nonlints]. Internal coordinates are defined [INTDEF keyword]
as the OH (1-2) and HCl (2-3) bond lengths and OHCl (1-2-3) bond angle. Vibrational
modes are treated by the Morse I approximation [MORSE, MORMODEL = morsei], with a
dissociation energy [DEMIN] of 0.16968172 Eh.
Polyrate I/O FILES
FILE NAME Polyrate FILE NAME
ohcltr1.dat poly.fu5 input data file
ohcltr1.fu6 poly.fu6 long output file
ohcltr1.fu14 poly.fu14 summary output file
ohcltr1.fu15 poly.fu15 summary output file
Polyrate 430
16.C.98. Test run ohcltr2
O + HCl → OH + Cl ICVT calculation using WKB-on-the-true-potential for
ground-state energies and Morse 1 anharmonicity for
excited stateenergies.
This sample run is the same as ohcltr1, except that the ground-state vibrational energy
levels are calculated using the WKB method on the true potential. All excited state
energy levels are computed using the Morse I approximation [MORSE, MORMODEL =
morsei], with a dissociation energy [DEMIN] of 0.16968172 Eh.
Polyrate I/O FILES
FILE NAME Polyrate FILE NAME
ohcltr2.dat poly.fu5 input data file
ohcltr2.fu6 poly.fu6 long output file
ohcltr2.fu14 poly.fu14 summary output file
ohcltr2.fu15 poly.fu15 summary output file
Polyrate 431
16.C.99. Test run ohcltr3
O + HCl(v=1) → OH + Cl Adiabatic excited-state calculation using WKB-on-the-true-
potential for the v=1 stretch energy and for the ground-state
bend energy and Morse 1 anharmonicity for excited
statebend energies.
This sample run is the same as ohcltr2, except that the reaction is for excited-state stretch
vibration. The stretch vibration is treated as adiabatic along the full reaction path
[STATE adiab] with quantum number v=1 specified using the STATEOPT keyword.
The excited-state energy level for the stretch vibration and the ground-state vibrational
energy level for the bend vibration are calculated using the WKB method on the true
potential. Bend excited state energy levels are computed using the Morse I
approximation [MORSE, MORMODEL = morsei], with a dissociation energy [DEMIN] of
0.16968172 Eh. The ICVT calculation is limited to –1.5 a0 < s < 1.0 a0.
Polyrate I/O FILES
FILE NAME Polyrate FILE NAME
ohcltr3.dat poly.fu5 input data file
ohcltr3.fu6 poly.fu6 long output file
ohcltr3.fu14 poly.fu14 summary output file
ohcltr3.fu15 poly.fu15 summary output file
Polyrate 432
16.C.100. Test run ohcltr4
O + HCl(v=1) → OH + Cl Partial-reaction-path (PRP) adiabatic excited-state
calculation using WKB-on-the-true-potential for stretch
energy and for the ground-state bend energy and Morse 1
anharmonicity for excited statebend energies.
This sample run is the same as ohcltr3, except that stretch vibraton is treated as adiabatic
in the v=1 state along the reaction path only up to s = –0.22 a0 and then in the ground
state for s>-0.22 a0. This is specified using the STATE diab keyword and specifying
transition state mode 2 in the first excited state before the diabatic switch and in the
ground excited state after the diabatic switch. Thermal treatment of the bend vibration
before and after the switch is explicitly indicated in the input. The energy level for the
stretch vibration and the ground-state vibrational energy level for the bend vibration are
calculated using the WKB method on the true potential. Bend excited state energy levels
are computed using the Morse I approximation [MORSE, MORMODEL = morsei], with a
dissociation energy [DEMIN] of 0.16968172 Eh. The ICVT calculation is limited to –1.5
a0 < s < 1.0 a0.
Polyrate I/O FILES
FILE NAME Polyrate FILE NAME
ohcltr4.dat poly.fu5 input data file
ohcltr4.fu6 poly.fu6 long output file
ohcltr4.fu14 poly.fu14 summary output file
ohcltr4.fu15 poly.fu15 summary output file
Polyrate 433
16.C.101. Test run ohcltr5
O + HCl → OH + Cl ICVT and MUCVT calculation using Morse 1
anharmonicity and internal coordinates
This sample run is the same as ohcltr1, except that microcanonical variational theory
(MUCVT) rate constants are also calculated. The primary and secondary fits use 1-point
and 3-point fitting [MUVTOPT, FIT= GAS13].
Polyrate I/O FILES
FILE NAME Polyrate FILE NAME
ohcltr5.dat poly.fu5 input data file
ohcltr5.fu6 poly.fu6 long output file
ohcltr5.fu14 poly.fu14 summary output file
ohcltr5.fu15 poly.fu15 summary output file
Polyrate 434
16.C.102. Test run ch3tr1
CH + H2 → CH3 VRC-VTST calculation
This sample run calculates the variable reaction coordinate variational transition state
theory rate constants by canonical variational theory, microcanonical variational theory,
and total energy and angular momentum resolved microcanonical variational theory. One
pivot point is assigned to each reactant. Pivot point for CH is assigned as the C atom, and
pivot point for H2 is the center of mass of H2. The range of reaction coordinate s is [1.3,
6.5] Å with a step size 0.2 Å. The number of Monte Carlo samples (keyword NMC) is set
to 100 for each dividing surface. Note that this number should be set to around 1000 in a
production run in order to have a much lower uncertainty of the Monte Carlo integration.
Polyrate I/O FILES
FILE NAME Polyrate FILE NAME
ch3tr1.dat poly.fu5 input data file
ch3tr1.fu6 poly.fu6 long output file
ch3tr1.fu15 poly.fu15 summary output file
Polyrate 435
16.C.103. Test run h3o2fu31tr1
H2O2 + H → H2O + OH TST with torsional treatment for H2O2 using the
segmented-reference Pitzer-Gwinn (SRPG) method
This sample run calculates rate constants by conventional TST. This run is used to show
the usage of the SRPG method for treating a torsion. The potential energy surface is
provided by the h3o2fu31tr1.fu31 file.
Polyrate I/O FILES
FILE NAME Polyrate FILE NAME
h3o2fu31tr1.dat poly.fu5 input data file
h3o2fu31tr1.fu31 poly.fu31 input data file
h3o2fu31tr1.fu6 poly.fu6 long output file
h3o2fu31tr1.fu15 poly.fu15 summary output file
Polyrate 436
16.C.104. Test run h3o2fu31tr2
H2O2 + H → H2O + OH TST with torsional treatment for H2O2 using the
segmented-reference Alyala-Schlegel (SAS)
method
This sample run calculates rate constants by conventional TST. This run is used to show
the usage of the SAS method for treating a torsion. The potential energy surface is
provided by the h3o2fu31tr2.fu31 file.
Polyrate I/O FILES
FILE NAME Polyrate FILE NAME
h3o2fu31tr2.dat poly.fu5 input data file
h3o2fu31tr2.fu31 poly.fu31 input data file
h3o2fu31tr2.fu6 poly.fu6 long output file
h3o2fu31tr2.fu15 poly.fu15 summary output file
Polyrate 437
16.C.105. Test run h3o2fu31tr3
H2O2 + H → H2O + OH TST with torsional treatment for H2O2 using the
reference Pitzer-Gwinn (RPG) method
This sample run calculates rate constants by conventional TST. This run is used to show
the usage of the RPG method for treating a torsion. The potential energy surface is
provided by the h3o2fu31tr3.fu31 file.
Polyrate I/O FILES
FILE NAME Polyrate FILE NAME
h3o2fu31tr3.dat poly.fu5 input data file
h3o2fu31tr3.fu31 poly.fu31 input data file
h3o2fu31tr3.fu6 poly.fu6 long output file
h3o2fu31tr3.fu15 poly.fu15 summary output file
Polyrate 438
16.C.106. Test run h3o2fu31tr4
H2O2 + H → H2O + OH TST with torsional treatment for H2O2 using the
Alyala-Schlegel (AS) method
This sample run calculates rate constants by conventional TST. This run is used to show
the usage of the AS method for treating a torsion. The potential energy surface is
provided by the h3o2fu31tr4.fu31 file.
Polyrate I/O FILES
FILE NAME Polyrate FILE NAME
h3o2fu31tr4.dat poly.fu5 input data file
h3o2fu31tr4.fu31 poly.fu31 input data file
h3o2fu31tr4.fu6 poly.fu6 long output file
h3o2fu31tr4.fu15 poly.fu15 summary output file
Polyrate 439
16.D. Summary of test runs
This section contains a summary of the test runs which make up the Polyrate test suite.
Analytic potential
ch5j1tr1 ch5j1tr2 ch5j1tr3 ch5j1tr4 ch5j1tr5 ch5j1tr6
ch5j1tr7 ch5j1tr8 ch5j1tr9 ch5j1tr10 ch5j1tr11 ch5j1tr12
ch5j2tr1 ch5j2tr2 ch5j2tr3 clhbrtr1 clhbrtr2 clhbrtr3
clhbrtr4 clhbrtr5 cmctr1 cwmctr1 cwmctr2 cwmctr3
h3tr1 h3tr2 h3tr3 h3tr4 ho2tr1 ho2tr2
ho2tr3 ho2tr4 oh3tr1 oh3tr2 oh3tr3 oh3tr4
oh3tr5 oh3tr6 oh3tr7 oh3tr8 oh3tr9 oh3tr10
hnitr1 h2nitr1 ch4otr1 cmctr3 ch5fu51tr1 nh3tr2
ohcltr1 ohcltr2 ohcltr3 ohcltr4 ohcltr5 ch3tr1
fu30
ch5fu30tr1 ch5fu30tr2 ch5fu30tr3 ch5fu30tr4 ch5fu30tr5 ch5fu30tr6
oh3fu30tr1 oh3fu30tr2 oh3fu30tr3 oh3fu30tr4 oh3fu30tr5 oh3fu30tr6
fu31
ch5fu31tr1 oh3fu31tr2 ohfu31tr1 h3o2fu31tr1 h3o2fu31tr2 h3o2fu31tr3
h3o2fu31tr4
fu40
ch5fu40tr1 ch5fu40tr2 ch5fu40tr3 ch5fu40tr4 ch5fu40tr5 ch5fu40tr6
oh3fu40tr1 oh3fu40tr2 oh3fu40tr3 oh3fu40tr4 oh3fu40tr5 oh3fu40tr6
IVTST-0 with fu29
ch5j2itr1 ch5fu29tr1 ch5fu29tr2 ch4ohtr2 ch4cltr1
IVTST-0 with fu50
ch5fu50tr1 ch4ohtr1
IVTST-1 with fu29
ch5j2itr2 ch4cltr2
Polyrate 440
VTST-IOC with analytic potential and fu50
ch5fu50tr2 ch5fu50tr3 cmctr2 ho2tr5 nh3tr1
VTST-IOC with fu30, fu31, or fu40 and fu50
ch5icfu30tr1 ch5icfu30tr2 ch5icfu31tr1 ch5icfu40tr1 ch5icfu40tr2
VTST-ISPE with fu30, fu31, or fu40 and fu51
ch5fu51tr1 cmctr3
Polyrate 441
17. DESCRIPTION OF FILES IN RELEASE OF VERSION 17
The source code is partitioned into 33 FORTRAN files. Note that a full Polyrate source
consists of everything in the 33 FORTRAN files that including modules and parameters.
A description of each Polyrate subprogram is given in Subsection 17.A.1. Subsection
17.A.2 briefly describes the subprograms SETUP and SURF, which must be supplied by the
user for runs that do not use any of the potentials provided for the test run suite. (Dummy
versions that can be used for runs with POTENTIAL = unit30, unit31, or unit40 are
in dumpot.f.) The input and output files for the sample runs are explained in Subsection
16.C. The Unix C shell scripts are explained in Subsection 15.A and Section 18. A list
of all the files in the distribution package can be found in Subsection 15.A.
The files polymq.F and polysz.F contain subprogram MXLNEQ for solving and inverting
sets of simultaneous linear equations and EISPACK subroutines for determining matrix
eigenvalues and eigenvectors. In the distributed version the machine precision variable
MACHEP is set equal to 1.0 1038 in the MXLNEQ subprogram and to 2-46 in the EISPACK
subprograms. We found these settings to be adequate for all machines on which we
tested the code.
If you received the Polyrate distribution in a tar format, then the files will automatically
be distributed into the default Polyrate directories as described in Section 15, except that
this manual may be in a separate file (not tarred with everything else).
17.A. FORTRAN files and subprograms, MODULE files, and PES subroutines
Subsection 17.A.1 contains an alphabetical list and brief descriptions of all the
subprograms that make up the Polyrate program, Subsection 17.A.2 describes the
MODULE files and the user-supplied potential energy subprograms, and Subsection 17.A.3
describes the FORTRAN files.
17.A.1. Polyrate subprograms
In many cases a more detailed description and some relevant references are given as
comments at the beginning of the FORTRAN code for each subprogram. Note that
subroutines may be divided into two groups, POLYRATE-proper routines and hooks
Polyrate 442
routines. Routines that start with a Y or have HOOK in the name are always part of the
hooks.
ABSORD
Order the lowest eigenvalues and eigenvectors according to absolute values.
ACALC
Dummy routine in place of the corresponding ACESRATE routine.
ACESET
Dummy routine in place of the corresponding ACESRATE routine.
AITKEN
Performs a Lagrangian interpolation of the effective reduced mass from the
reaction-path Hessian grid.
AITKF2
Checks the Aitken interpolation for "bad" values, i.e., interpolants that do not lie
within the original range of the data.
AITKNF
Performs Aitken interpolation.
ALFCT
Computes the logarithmic values of factorials of even integers used in the
calculation of the Bernoulli numbers.
ANCOEF
Computes the anharmonicity coefficients xij and the constant term (E0) from
dimensionless normal coordinate force constants evaluated previously by
subprogram GRADDR, and then calculates the vibrational ground-state energy
and fundamentals from the anharmonicity coefficients and the constant term.
ANGL
Function that calculates the angle i-j-k.
ANGLCS
Function that calculates the sine and cosine of the valence angle between two
difference Cartesian vectors.
ANGLV
Calculates the angle between two vectors.
Polyrate 443
ANHARM
Computes anharmonicities for bound normal modes. The anharmonicity option is
selected by the anharmonicity keywords.
ANHDER
Computes the 3rd and 4th derivatives along the generalized normal modes.
ARMUEF
Calculates the argument of the exponential in equation 19 of Ref. 48 in Sect. 21
for the interpolation of the effective mass for CD-SCSAG tunneling.
ARMUEF1
Calculates CDSC for the extrapolated points in IVTST-M with the hooks.
ARRSM
Calculates the moment of inertia for the points along the reaction path given in
fu31 and reorders them according to the value of s.
ARRSV
Reorders the value of VMEP(s) given as input in fu31 according to s.
ASYMALP
Calculates the direction cosines for an asymmetric gyrator.
ASYMCAL
Prints the moment of inertia of a group of asymmetric gyrators.
ASYMENT
Calculates the moment of inertia of an asymmetric gyrator.
ASYMNZD
Sets up the calculation of moment of inertia of an asymmetric gyrator.
ASYMRMI
Calculates the moment of inertia of an asymmetric gyrator.
AVERJ
Calculate an integral over all possible orientation of the angular momentum
vector J with its length fixed in the evaluation of the number of available states.
BANGLE1
Calculates the Wilson B-matrix (R/X) for bending.
Polyrate 444
BCALC
Calculates the curvature components and the total curvature for the small-
curvature semiclassical adiabatic tunneling calculations.
BCALCP
Calculates Page-McIver curvature factors BmF.
BCALC0
Calculates the small-curvature effective mass at the saddle point by linear
interpolation.
BTORSN
Calculates the Wilson B-matrix (R/X) for a torsion.
BMAT
Calculates the Wilson B-matrix, R/X, where R are the curvilinear internal
coordinate vectors and X are the Cartesian coordinate vectors.
BMAT1
Forms the Wilson B-matrix row corresponding to a linear stretch coordinate
between atom j and atom i. The input is in the form of difference Cartesians.
BMAT2
Forms the rows of the Wilson B-matrix corresponding to a bent triatomic.
BMAT5
Forms the Wilson B-matrix rows corresponding to degenerate linear bends. The
input is in the form of two difference Cartesians defining the linear triatomic. The
definitions of the bends are those of Hoy et al. (Mol. Phys. 24, 1265 (1972)).
BMAT5X
Forms the Wilson B-matrix rows corresponding to degenerate linear bends. The
input is in the form of two difference Cartesians defining the linear triatomic by
first determining a transformation matrix to rotate the coordinate system such that
the molecule lies along the Z axis.
BIMAT
Calculates the generalized inverse of the Wilson B-matrix.
BTEN1
Forms the Wilson B-matrix 2nd derivative elements for a bond-length curvilinear
internal coordinate in terms of its first derivatives and magnitudes of difference
Cartesians.
Polyrate 445
BTEN2
Computes the bent triatomic 2nd derivative Wilson B-matrix elements.
BTEN5
Defines the 2nd derivative Wilson B-matrix elements for the degenerate linear
bend in terms of the difference Cartesian vectors that define its bonds.
BTEN5X
Defines the 2nd derivative Wilson B-matrix elements for the degenerate linear
bend in terms of the difference Cartesian vectors that define its bonds so that the
molecular frame has the linear bend along the Z axis.
BTENTR
Transforms the Wilson B-matrix elements from difference Cartesians to
Cartesians.
BTENS
Calculates the tensor (X/R•R2/X
2•X/R).
BOLTZ
Performs the Boltzmann average of the tunneling probability by a numerical
integration with respect to E.
BRENT
Implements Brent's line minimization method. See Ref. 14 in Sect. 22.
BRNULI
Computes Bernoulli numbers used in the calculation of the WKB phase integral
for a double-well potential.
CALCS
Computes the minimum distance between two geometries along the reaction path
measured as a straight line between them.
CALCUB
Calculates the coefficients for the cubic polynomial used in the IVTST-M interpolation of VMEP(s) for unimolecular reactions.
CASE
Function that takes a string of 80 characters and converts the upper case letters in
the string to lower case letters.
Polyrate 446
CENTER
Translates the center of mass of the system to the origin. Also calculates the
determinant of the moment of inertia tensor, which is equal to the product of the
three principal moments of inertia, since they are the eigenvalues of this matrix.
CENTR1
Determines the relative index assignments for a linear triatomic system (i -j-k).
Atom i is placed in the center and the j-k assignments are made arbitrarily.
CENTRAL
Determines which atom is the central atom for a bent triatomic by using bond
lengths, and calculates the bond angle.
CFLOAT
Function that takes a character string that contains a floating point number and
converts it to a floating point number as defined by standard FORTRAN
conventions.
CHKFRE
Checks if any of the vibrational frequencies are zero or imaginary.
CHKUP
Retrieves 3rd-order dimensionless normal coordinate force constants needed for
calculating the vibrational ground-state energy and fundamentals for simple
perturbation theory calculations.
CLASS
Finds the recursion relation for various classes of orthogonal polynomials used to
find the nodes in Gaussian-type quadratures.
CMS
Calculates the center of mass of a subset of the system.
COG
Defines a cut-off Gaussian correction function.
COHBT1
Defines a cut-off hyperbolic tangent correction function.
COHBT2
Defines a cut-off hyperbolic tangent correction function.
COLSHF
Performs shifting of Hessian grid data in the storage arrays.
Polyrate 447
CONOUT
Prints out the curvilinear internal coordinates.
CONV40
Converts the geometries, gradients, and Hessians to atomic units.
CORTRM
Calculates Coriolis constants.
COSINE
Modified cosine function.
CROSSPROD
Calculate cross product of two vectors.
CRVVEC
Computes the curvature vector when unit40 input is used.
CUBST
Evaluates quantities necessary for the cubic-starting algorithm.
CUBIC
Finds the real root of ax3+ bx2+ cx + d = 0 closest to a given x value.
CUBIC2
Finds all roots (real and complex) of ax3+ bx2+ cx + d = 0.
CUSSPL
Spline fits the GGT,0(s) curve and finds the maxima and minima along the curve
for a CUS calculation.
CVCOOR
Driver for the curvilinear internal coordinate bound-state analysis of non-linear
polyatomics.
DAXPY
BLAS routine calculates yx+c .
DATTIM
Calls system-dependent subroutines DATE and TIME and writes the current date
and time.
DEFALT
Sets the defaults for all the parameters and variables used in POLYRATE. The
defaults for each different section of input is set in a separate subprogram for
clarity.
Polyrate 448
DEFENG
Sets the defaults for keywords used in the ENERGETICS section.
DEFGEN
Sets the defaults for keywords used in the GENERAL section.
DEFLT40
Determines if the needed fu40 keywords were read for the IOPth species. Default
values are assigned when necessary.
DEFOPT
Sets the defaults for keywords used in the OPTIMIZATION section.
DEFPAT
Sets the defaults for keywords used in the PATH section.
DEFRAT
Sets the defaults for keywords used in the RATE section.
DEFSEC
Sets the defaults for keywords used in the SECOND section.
DEFSTA
Sets the defaults for keywords used in the all the stationary point sections.
DEFTUN
Sets the defaults for keywords used in the TUNNEL section.
DERIV2
Calculates the Hessian matrix by using a quadratic fit to the potential energy
surface. Only the potential is used, not its first derivatives.
DERV
Calculates the curvature vector related to third derivatives for IVTST calculations.
DERV24
Computes the second derivatives of the potential by fitting the analytic first
derivatives to a fourth-order polynomial around the desired location and then
taking the derivative of this polynomial.
DERVAG
Evaluates the first derivative of an n-dimensional point by the two-point central
difference method.
DFGN31
Polyrate 449
Set defaults for a fu31 file.
DGAMMA
Evaluates the gamma function of order n 3.
DGEDI
Computes the determinant and inverse of a matrix using the factors computed by
DGEFA.
DGEFA
Factors a double precision matrix by Gaussian elimination.
DIATOM
Computes the equilibrium properties for a diatomic reactant or product treated as
a Morse oscillator.
DIGISTR
Function that transform a three digits integer into a string with 3 characters.
DIST
Function that calculates an interatomic distance.
DPMPAR
A service routine for HYBRD1 that computes machine precision.
DOGLEG
A service routine for HYBRD1 that determines the convex combination x of the
Gauss-Newton and scaled gradient directions that minimizes (ax - b) in the least-
squares sense, subject to the restriction that the Euclidean norm of dx be at most
delta.
DOPNM
Calculates the steepest-descent path and the generalized normal modes along the
MEP.
DOREPR
Calculates the reactant and product properties.
DOREST
Prepares a restart calculation (i.e., reads data from unit fu1, etc.).
DORODS
Subroutine used to setup a RODS or VRP(ESD) calculation.
Polyrate 450
DORPH
Prepares the potential energy routines and sets up the MEP interpolation
information for an electronic structure input file calculation.
DOSAFR
Calculates the saddle point frequencies.
DOSAGE
Calculates the saddle point geometry.
DDOT
BLAS routine computs the dot product of two vectors.
DOTPRD
Computes the dot product between two vectors.
DPR123
Computes the dot product between two vectors. First vector points from atom 2
to atom 1; second vector points from atom 2 to atom 3.
DPSWAP
Swaps two double precision numbers.
DSCAL
BLAS routine scales a vector by a constant.
DSWAP
BLAS routine interchanges two vectors.
EBND
Computes the energy of a level of a quadratic-quartic potential by the
perturbation-variation method of Truhlar.
ECKARS
Interpolates the classical potential curve (IOP = 1) or the ground-state vibrationally
adiabatic energy curve (IOP = 2).
ECKART
Defines an Eckart correction function.
ECKRT
Interpolates frequencies with an Eckart or a hyperbolic tangent function.
EHOOK
The driver for the energy routines in the modular version of POLYRATE.
Polyrate 451
EFFBATH
Computes the solvent contribution for the nonequilibrium solvation
approximation.
EFMAIN
The driver for the eigenvector following algorithm.
EFPHES
Prints the Hessian matrix in eigenvector following algorithm.
EFORMD
Forms geometry step by eigenvector following algorithm.
EFOVLP
Determines the overlap of the geometry steps in the eigenvector following
algorithm.
ELLIP
Computes elliptic integrals of the first and second kinds.
ELRPH
Evaluates generalized normal mode frequencies along the MEP when electronic-
structure input is used [POTENTIAL = unit30 or unit40].
ENDRODS
Subroutine used to finish a RODS or VRP(ESD) calculation.
ENDSLP
TSPACK subroutine that estimates the first derivative at the edges of the spline-fit
interval to be used as the two extra conditions of the global spline under tension.
ENORM
Calculates the norm of a vector x.
ENROUT
Writes reaction energetics information to FORTRAN unit fu6.
EPARTI
Function that computes the electronic partition function for IVTST calculations.
EPART
Computes the electronic partition function.
ERF
Calculates the error function.
Polyrate 452
EVIB
Calculates vibrational energy levels.
EWKB
Uses a Chebyshev quadrature to compute the primitive WKB approximation to
the energy of a vibrational level of a quadratic-quartic potential.
EXPND
Expands triangular matrix A to square matrix B.
EXTRAP
Provides simple exponential extrapolations to the asymptotic values of quantit ies
used in tunneling calculations.
EXTRP40
Sets the values for extrapolation when using unit fu40 input.
EXTRP
Fits a straight line to two points and carries out interpolations or extrapolations.
F1DI
Evaluates the function VALVAG for LINMNR.
F1DIM
Computes the one-dimensional energy for use in line minimization subroutines.
FACORD
Orders the force constants scaling factors according to the actual sequence of the
curvilinear internal coordinate when FCSCALE is used.
FCINPT
Closes all the input files used in READ5.
FCMEP
Closes all the input and output files used in the MEP calculation.
FCN
Calculates an Eckart or a hyperbolic tangent function to be passed into the non-
linear equation solver.
FCRATE
Closes all the input and output files used in the rate constant and the tunneling
calculations.
FCSCL
Polyrate 453
Scales diagonal elements of the force constant matrix in curvilinear internal
coordinates by corresponding scaling factors when FCSCALE is used.
FDIAG
Diagonalizes the force constant matrix and, optionally, prints out generalized
normal mode information.
FDIAG2
Diagonalizes the Cartesian force constant matrix for Hessians from unit 29 input
and, optionally, prints out generalized normal mode information.
FDJAC1
A service routine for HYBRD1 that computes a forward-difference approximation
to the n x n Jacobian matrix associated with a specified problem of n functions in
n variables. If the Jacobian has a banded form, then function evaluations are saved
by only approximating the nonzero terms.
FICLSE
Closes a file given the status with which to close the file and the FORTRAN unit
number to which the file is linked.
FINDL
Calculates the value for the RPL keyword in a VTST-IC input file (fu50) from a
lower-level calculation.
FINDLV
Calculates the range parameter for an Eckart function.
FINOUT
Computes and prints out the final set of rate constants. Also obtains activation
energies and bottleneck properties and analyzes the ratio of transition state theory
results to those of canonical variational transition state theory.
FIOPEN
Opens all files needed for a given calculation except for the main input and the
main output files (i.e., the files linked to FORTRAN units fu5 and fu6).
FITMAX
Finds the maximum in the adiabatic potential curve and the generalized free
energy of activation curve using 3- and 5-point fits.
FITMX
Finds the maximum of function f with a 5-point fit.
Polyrate 454
FIVFT
Computes a quartic fit through five points for IVTST.
FIVPT
Computes a quartic fit of F = ax4+ bx3+ cx 2+ dx + e to five points.
FORMA
Forms the generalized inverse of the B-matrix by the Pulay prescription.
FORMF
Forms the product ATFA, where A is the A-matrix and F is the Cartesian force
constant matrix.
FORMF2
Forms the second term of curvilinear internal force constant matrix.
FORMG
Forms the G matrix.
FORMBT
Forms one xyz-band of the transformation matrix from Cartesian coordinates to
difference Cartesians.
FRPRMN
Conjugate gradients minimization subroutine.
FRSORT
Sorts a set of frequencies into ascending or descending order.
GAUSQD
Calculates the weights and abscissa for N-point Gauss-Legendre quadrature.
GAUSSQ
Computes the nodes and weights for Gaussian-type quadrature.
GBSLVE
For a symmetric tridiagonal n n matrix A, this subroutine finds the component n
of the n-dimensional vector v such that Av = c, where c is a vector of all zeros
except for 1 in the n-th position.
GBTQL2
Finds the eigenvalues and the first components of the eigenvectors of an
asymmetric tridiagonal matrix by the implicit QL method.
Polyrate 455
GEMM
Performs fast matrix multiplication. From the BLAS library.
GENSEC40
Reads and processes the GEN40 section of the unit fu40 input.
GETFRQ
Obtains vibrational frequencies in cm-1
and generalized eigenvectors.
GFDIAG
This routine effectively diagonalizes the unsymmetric GF-matrix, formed by
product of G and F. The method is given by Macintosh and Michaelian (Can. J.
Spectrosc. 24, 65 (1979)). Only symmetric matrices are diagonalized here. the
GF product is never explicitly formed.
GFDIA2
This routine effectively diagonalizes the unsymmetric, rectangular GF matrix by
generalized inverse G matrix method. The method is given in P. Pulay,; G.
Fogarasi, J. Chem. Phys. 1992, 96, 2856.
GHOOK
The driver for the first derivative routines in the modular version of POLYRATE.
GIVTST
Driver for zero- and first-order interpolated VTST (the global approach) as
described in J. Chem. Phys. 95, 8875 (1991).
GRAD
Evaluates derivatives along normal mode (or generalized normal mode)
directions.
GRADDR
Calculates 3rd- and 4th-order dimensionless normal coordinate force constants.
GSETA
Dummy routine in place of the corresponding ACESRATE routine.
GSETM
Geometry optimization calculations needed when Polyrate is used with MOPAC.
GSETP
Geometry optimization calculations needed when Polyrate is used with an
analytic surface.
Polyrate 456
HBT
Calculates the hyperbolic tangent at sMEP.
HEADR
Prints out the program header.
HHOOK
The driver for the second derivative routines in the modular version of POLYRATE.
HINDRT
Calculates the moment of inertia for internal rotation.
HINDRT1
Calculates the moment of inertia for internal rotation of an asymmetric gyrator.
HQSC
Semiclassical solution of a harmonic-quartic potential.
HRPART
Calculates the partition functions using the hindered-internal-rotator
approximation.
HRSET
Setup calculation of hinder rotor partition function.
HVAL
TSPACK subroutine that evaluates a Hermite interpolatory tension spline at a
point.
HYBRD
A service routine for HYBRD1.
HYBRD1
Finds a zero of a system of n nonlinear functions in n variables by a modification
of the Powell hybrid method.
ICFDRP
Driver of the curvilinear internal coordinate bound-state analysis for reactants and
products.
ICFDIAG
Driver for the curvilinear internal coordinate bound-state analysis of triatomics.
Polyrate 457
ICINT
Function that takes a character string which is really an integer and converts it to
an integer. Error checking that is not possible using ichar is done.
ICODAL
Function that translates a set of alphanumeric characters into an integer code.
ICOUTRP
Prints out the curvilinear internal coordinates for reactants and products.
ICSAVE
Copies frequencies and eigenvectors for bound modes from curvilinear internal
coordinate work spaces to the locations used by Cartesian coordinate procedures.
ICSVRP
Copies the bound-state analysis results from the curvilinear internal coordinate
work spaces to the locations used by Cartesian coordinate procedures.
IDAMAX
BLAS routine finds the index of element having maximum absolute value.
IMOM40
Computes the moment of inertia.
INTCOR
Defines the curvilinear internal coordinates for reactants and products by splitting
the global connectivies into subsets.
INTERSC
Finds out the intersection of two integer arrays.
INTF31
Subroutine that reorders the information on stationary points taken from fu31 and
puts it on the correspondent arrays.
INTRVL
TSPACK function that locates the interval in the input data for a spline fit that
contains a certain point.
INVRT
Inverts a one-dimensional array of size N.
INVRT2
Inverts a two-dimensional array of size N1, N2.
Polyrate 458
INVRT3
Inverts a three-dimensional array of size N1, N2, N3.
INERTA
Calculates the moment of inertia for a linear molecule or a diatomic, or the
product of the moments of inertia for a non-linear molecule in au.
INITVRC
Initializes the array IATSV(I,J) for the generalized transition state in variable
reaction coordinate calculations because START section is not give in the fu5 file.
INITZE
Initializes some of the variables and arrays.
INTAB
Writes out a table of all the input parameters.
INTABS
Writes out a table of all the input parameters associated with the stationary point
sections.
INTEGR
Integration driver for the PATH subroutine.
INTEUL
Performs Euler steepest-descents integration.
INTFNC
Calculates and returns the negative of the normalized gradient for the path
integration.
INTPM
Page-McIver reaction path algorithm..
INTPM2
Computes s /t for the Page-McIver method.
INTRPL
Calls POLFIT to do polynomial interpolation for a given quantity.
Polyrate 459
IRCX
Intrinsic-reaction-coordinate pathfinder, using the method of Schmidt, Gordon,
and Dupuis.
IRFTG0
Computes the information necessary for dealing with the frequencies, Hessians,
and curvature vectors for unit fu40 input.
IRPHZ
Does interpolations for the zero-order IVTST calculations.
IRPH
Does interpolations for the first-order IVTST calculations.
ISWAP
Swaps two integers.
IVTMA
Interpolates the exponent for calculating CDSC by IVTST-M through the hooks.
IVTMD
Calculates the extrapolated points with IVTST-M through the hooks.
IVTMH
Sets up the parameters required for IVTST-M through the hooks.
IVTST0
Calculates the classical (i.e., Born-Oppenheimer) potential energy curve and the
adiabatic ground-state potential energy curve along the reaction path in a zero-
order VTST-IOC calculation.
JACSCF
Computes all eigenvalues and eigenvectors by the Jacobi method.
KAPA
Calculates transmission coefficients for IVTST calculations.
KAPPAS
Calculates the transmission coefficients using the uniform semiclassical WKB
method (MEPSAG) and the small curvature method (SCSAG).
KAPVA
Calculates the tunneling corrections for a set of temperatures.
Polyrate 460
KG1
Nodes and weights for Kronrod quadrature.
LCG34
Calculates the tunneling probabilities PLCG34 (E) by the LCG34 method.
LCGIT
Builds the grid for the 1D spline under tension.
LCGNAD
Defines the limit between adiabatic and nonadiabatic regions for the LCT3 and
LCT4 methods.
LCGRD
Builds a 2D rectangular grid from selected points of the PES.
LCGSRT
Sorts the uniformized LCG3 or LCG4 probabilities.
LCGTHE
Calculates the primitive tunneling amplitude Ttun˜ s 0 ,np( ) by integration over the
straight-line LCG3 or LCG4 tunneling path using both Gauss-Legendre
quadrature and the trapezoidal rule.
LCGTR
Transforms a point of the PES to a point of the 2D rectangular grid.
LCNORM
Calculates the generalized normal mode coordinates corresponding to the scaled
displacements along the LCG3 or LCG4 tunneling path. These coordinates are
needed for eq. (14) of Ref. 20 in Sect. 21.
LCNWTN
Performs a Newton root search to determine the s value corresponding to a point
along the LCG3 or LCG4 tunneling path, using eq. (22) of Ref. 20 in Sect. 21.
LCPATH
Calculates the mass-scaled Cartesian coordinates of the LCG3 or LCG4 tunneling
path as given in eq. (8) of Ref. 20 in Sect. 21.
LCPROB
Calculates the uniformized LCG3 probabilities from the primitive values
Pprim
LCG3E( ) using eq. (30) of Ref. 20 in Sect. 21.
Polyrate 461
LCPROJ
Calculates the projections of the generalized normal mode coordinates onto the
LCG3 path using eq. (14) of Ref. 20 in Sect. 21.
LCSET
Sets up the LCG3 tunneling path and calculates the angle between the MEP and
the tunneling path [eq. (12) of Ref. 20 in Sect. 21] along with the vibrational
period of eq. (17) of Ref. 20 in Sect. 21.
LCSINT
Performs the numerical integration over tunneling termini along the reaction path
as given by eq. (9) of Ref. 20 in Sect. 21.
LCSTX
Sets up the tunneling path for excited final states and determines the highest
excited state involved in LCG3 calculations.
LCTP
Determines the ending terminus of the tunneling path for a given excited state of
the LCG3 exit arrangement and a given initiating terminus ˜ s 0 using the resonance
condition.
LCTV4
Searches for a LCT4 nonadiabatic region within a LCG3 adiabatic region.
LCVCOR
Calculates the effective potential for the nonadiabatic region in an LCG3
calculation as given in eq. (28) of Ref. 20 in Sect. 21.
LCVIB
Calculates the vibrational zero-point energies of eq. (5) of Ref. 20 in Sect. 21.
LCVMOD
Calculates the zero-point energy and potential for a given normal mode in an
LCG3 calculation.
LCXINT
Calculates the integrand in the phase integral along the adiabatic segments of an
LCG3 tunneling path.
LCXTAU
Calculates the vibrational period, , for LCG3 calculations as given by eqs. (17)
and (18) of Ref. 20 of Sect. 21.
Polyrate 462
LCZCRT
Determines which region (adiabatic or nonadiabatic) a given point on an LCG3
tunneling path is in by using eqs. (23) and (24) of Ref. 20 in Sect. 21.
LIN
Solves a set of simultaneous linear equations.
LIN2
Solves two simultaneous linear equations in the matrix form Ax = b.
LININT
Does the linear interpolation.
LINMNR
Finds the minimum along a given direction.
LINMN
One-dimensional minimization search.
LOCATE
Determines the indices on the grid of reaction path coordinates corresponding to a
point on the LCG3 tunneling path determined by LCNWTN.
LOCS
Called by AITKF2 to locate the s value about which to center the interpolation
grid. The grid is centered about the closest point on the Hessian grid.
LOPT40
Translates the GEN40 input keywords to LOPT values.
LSAME
Service routine for GEMM.
LUDCMP
Performs an LU decomposition using an algorithm from W. H. Press, B. P.
Flannery, S. A. Teukolsky, and W. T. Vetterling, Numerical Recipes (Cambridge
University Press, Cambridge, 1986), p. 31.
LUBKSB
Service routine for LUDCMP.
MAIN
Driver for POLYRATE. The main input and output files (i.e., those files linked to
FORTRAN units fu5 and fu6) are opened in this subprogram.
Polyrate 463
MATINV
Performs matrix inversion using LU decomposition routines.
MATX
A general-purpose matrix multiplication routine.
MEPINV
Stores the information saved as functions of the reaction coordinate in order of
increasing s by inverting the order of storage.
MEPOUT
Prints MEP information to the long output file, i.e., to unit fu6.
MEPSRT
Does a bubble sort of the MEP information in order of increasing s.
MNBRAK
Finds an interval which contains a minimum.
MOPEG
Dummy routine to disable the keyword MOPAC in POLYRATE.
MOPHES
Dummy routine to disable the keyword MOPAC in POLYRATE.
MOPOPT
Dummy routine to disable the keyword MOPAC in POLYRATE.
MOPSET
Dummy routine to disable the keyword MOPAC in POLYRATE.
MTINV2
Performs matrix inversion using singular value decomposition routines
MUCDSC
Computes the centrifugal-dominant small-curvature effective mass.
Polyrate 464
MUSC
Computes the SCSAG effective mass.
MUSCCD
Computes the CD-SCSAG effective mass.
MXLNEQ
Solves a set of simultaneous linear equations in the matrix form Ax = b, and
evaluates the determinant of A.
NEARWC
computes the nearest reactant or product endpoint used in frequency interpolation .
NEWT
Does a Newton-Raphson search for a stationary point.
NEXTPT
Computes the next point on the MEP.
NORMOD
Computes generalized normal mode frequencies and directions.
NOROUT
Prints out generalized normal mode information.
NOST31
Processes the information about non-stationary points along the reaction path.
NSTATE
Calculates the total number of accessible states in LCG3 calculations that include
contributions from tunneling into excited states.
NUMFRQ
Calculates the number of internal vibrations.
OBTSRT
Compares two elements and stores the bigger one.
OHOOK
The driver for the geometry optimization routines in the modular version of
POLYRATE.
OPENFI
Opens a file given the unit number, the status, and the file name.
Polyrate 465
OPT50
Checks for any conflicts in the options for the VTST-IOC calculations.
OPT50C
Checks for consistency between the VTST-IOC options chosen in the unit fu50
input.
OPTION
Checks for consistency between the options chosen in the unit fu5 input and
writes out information about the options selected.
ORDS31
Reorders the information stored on the array save31 containing all the information
given as an input in fu31.
OVRLP
Computes overlaps between old and new normal mode eigenvectors and warns if
a crossing has occurred.
PATH
Calculates the reaction path.
PHID
Computes the phi function needed for uniform semiclassical quantization of a
double-well potential.
PHSINT
Computes the phase integral for the WKB method.
PMOI
Calculate priccipal moment of inertia and their unit vector along the ith principal
axis for each reactant or complex of reactants
POLINT
Uses Neville's algorithm to interpolate a given quantity.
Polyrate 466
POLYAT
Calculates the equilibrium properties of a linear or a nonlinear polyatomic
reactant or product.
PRCORD
Prints the bond lengths, bond angles, and dihedral angle along the reaction path.
PREGPT
Spline fits s, V, and I-1 for IVTST-M calculations carried out through the hooks.
PREP
The driver for all the preparation routines in the modular version of POLYRATE.
PREPJ
The driver for all the preparation routines needed by REACT1, REACT2, PROD1,
PROD2, START, and PATH. See Sect. 8.C.
PRMEP
Prints extra MEP information to units fu25-fu27.
PRNTBT
Prints the B-matrix stored in lower triangular form in clusters of 5 rows.
PRNTFC
Prints a lower triangular matrix (in clusters of 5 rows).
PROJTI
Forms the projection operator and calculates the projected Cartesian force
constant matrix for IVTST calculations.
PROJCT
Calculates the projected force constant matrix and normalized gradient.
PROJF
Forms the projection operator and projects out the gradient from the curvilinear
internal force constant matrix.
PRSQ
Prints out a square matrix.
PSAG
Locates points (translational turning points) where the energy is equal to the
adiabatic potential and then computes the imaginary-action integral.
Polyrate 467
PSATP
Finds turning points on the adiabatic barrier.
PSATP2
Finds turning points on the adiabatic barrier.
PSATX
Finds turning points on the adiabatic barrier.
PSATX2
Finds turning points on the adiabatic barrier.
PTORS
Function that calculates the torsion angle i-j-k-l.
PTQVIB
Calculates vibrational partition functions by simple perturbation theory using the
ground-state energy and fundamentals. [See Ref. 23 in Sect. 21 for the equations
without Coriolis terms in E0 and see Ref. 35 in Sect. 22 for the Coriolis
contributions to E0.].
PTSEC40
Reads and processes the POINT40 sections in the unit fu40 input.
PYC1
TSPACK subroutine that employs a three-point quadratic interpolation method to
compute local derivative estimates associated with a set of data points. The
derivatives are chosen so that the Hermite interpolatory tension spline fulfils the
user selected end conditions.
PYC1P
TSPACK subroutine that employs a three-point quadratic interpolation method to
compute local derivative estimates associated with a set of data points. The
derivatives are chosen so that the Hermite interpolatory tension spline fulfils the
defaulted end conditions.
PYC2
TSPACK subroutine that solves a linear system for a set of first derivatives
associated with a Hermite interpolatory tension spline. The derivatives are chosen
so that the Hermite interpolatory tension spline fulfils the user selected end
conditions.
PYC2P
TSPACK subroutine that solves a linear system for a set of first derivatives
associated with a Hermite interpolatory tension spline. The derivatives are chosen
Polyrate 468
so that the Hermite interpolatory tension spline fulfils the defaulted end
conditions.
PYCOEF
TSPACK subroutine that computes the coefficients of the derivatives in the
symmetric diagonally dominant tridiagonal system associated with the C-2
derivative estimation procedure for a Hermite interpolatory tension spline.
QFORM
Computes the QR factorization.
QQPOT
Fits the quadratic-quartic potential to two points along the generalized normal
coordinate using two given distances.
QRFAC
This is a service routine for HYBRD1 that uses Householder transformations with
column pivoting (optional) to compute a QR factorization of the m x n matrix A.
QRSENE
Calculates the quantized reactant eigenstates for tunneling.
QSLVE
Computes a quadratic fit to the function values at two points and the derivative at
one point, and uses the fit to perform an interpolation.
QTQVIB
Calculates the quantized reactant-state partition functions.
QUADFT
Computes a quadratic fit to three points.
QUADR
Solves a quadratic equation.
QUADTW
For a function y (x) = A + B (x–C)2, finds B and C from the given information.
RBASIS
Dummy routine in place of the corresponding ACESRATE routine.
RBATH
Reads the keyword options for the BATH keyword in PATH section.
Polyrate 469
R1UPDT
A service routine for HYBRD1.
R1MPYQ
A service routine for HYBRD1.
RACES
Reads the ACES namelist options.
RALL31
Reads all the data from fu31 and store it in the save31 array.
RATE
Computes the generalized free energy of activation curves and rate constants.
RAN1
Random number generator from Numerical Recipes.
RANALY
Reads the temperatures at which a detailed analysis is desired.
RATOMS
Reads the atomic symbols and optionally the masses.
RCNST
Reads the coordinates that will be held constant in any optimization of a
stationary point geometry.
RD40EXTR
Reads the EXTRAP40 section of the file fu40 input.
RD40GEN
Reads the GEN40 section of the file fu40 input.
RD40RP
Reads the reactants and products sections of the file fu40 input.
RDETIL
Reads the LCG3 output details information.
RDIATM
Reads the diatomic options for stationary points.
Polyrate 470
RDIFFU
Reads the diffusion coefficients or coupling constants for the nonequilibrium
solvation calculation.
RDHESS
Reads a Hessian matrix from file fu40.
RDLN
Reads a line from an input file without conversion.
REACT
Computes the geometry and properties of a reactant or product.
REACTCOM
Calculate center of mass for reactants
READ5
Reads input from the file linked to FORTRAN unit fu5.
READIC
Reads the VTST-IOC correction data from the file linked to FORTRAN unit
fu50.
READINT
Reads INTDEF keyword information to get the connectivities.
READLN
Reads a line from an input file and converts all characters to uppercase.
REARG1
Rearranges a set of frequencies to an order that is input by the user.
RECS31
Recalculates all the values of s given in fu31 as distances along straight lines
between two consecutive geometries.
REDGEO
Determines the geometry of the reactant, product, or saddle point, i.e., linear or
nonlinear, and the number of degrees of freedom.
Polyrate 471
REDMU
Evaluates the effective mass for a given value of s for IVTST as described in J.
Chem. Phys. 95, 8875(1991).
REFOPT
Reads the options for eigenvector following algorithm.
RELEC
Reads the electronic degeneracies for stationary points.
RENERG
Reads the ENERGETICS section of the file fu5 input.
REPFL
Replaces the low-frequency mode along the path when the IVTST0FREQ keyword
is used.
RES1
Reads the variables for the Euler-with-stabilization (ES1) integrator.
RESTOR
Reads information from the file linked to FORTRAN unit fu1 for a restart rate
constant calculation.
RESTRT
Writes information to the file linked to FORTRAN unit fu1 for a restart rate
constant calculation.
REXTRP
Reads the EXTRAP section of the file fu5 input.
REZERO
Reads the input for the zero of energy.
REZERU
Reads the unit for the zero of energy.
RFCFAC
Reads FCSCALE keyword information to get the force constant scaling factors
when FCSCALE is used.
RFREQ
Reads frequencies from unit fu29 for IVTST calculations.
RGEM31
Polyrate 472
Reads the options for geometry input in fu31.
RGEN
Reads general information for IVTST calculations from unit fu29.
RGEN31
Reads the options in the general section of an fu31 input file.
RGENER
Reads the GENERAL section of the file fu5 input.
RGEOM
Reads the initial geometry for reactants or products.
RGRD
Read gradient from unit fu29 for IVTST calculations.
RGRD31
Reads the options for gradients input in fu31.
RGSAD
Reads the initial geometry for the saddle point or starting geometry.
RGSPEC
Reads the range of s for which the generalized free energy curve is to be
computed.
RGSZM
Reads the initial geometry for the saddle point or starting geometry using z-matrix
form.
RGTEMP
Reads the range of s values for each temperature for which the generalized free
energy curve is to be computed.
RGZMAT
Reads the initial geometry for the saddle point or starting geometry using z-matrix
form. This is used only when the geometry optimization is done using ACES.
RHESS
Reads Hessians from unit fu29 for IVTST calculations.
RHES31
Reads a Hessian matrix from fu31.
Polyrate 473
RHESSC
Reads HESSCAL options from unit fu5.
RHFSEC
Checks whether frequencies or Hessians are to be read.
RHSS31
Reads the options for Hessian input in fu31.
RICOPT
Reads the VTST-IOC options.
RLCT
Reads the information for large-curvature tunneling calculations.
RLINE
Utility program for reading a line of input and parsing off extra spaces and
comments.
RLOWFR
Reads the information given by the LOWFREQ keyword.
RMUVT
Reads VT options.
ROPT
Reads the OPTIMIZATION section of the file fu5 input.
ROPT31
Reads the general section of an incomplete fu31 file and sets the options for
writing it.
ROPTOP
Reads the options for the OPTIMIN and OPTTS keywords.
RPART
Computes the classical rotational partition function.
RPARTI
Computes the classical rotational partition function for IVTST calculations.
RPATH
Reads the PATH section of the file fu5 input.
RPH31
Sets up the defaults and routes for reading an fu31 file.
Polyrate 474
RPH40
Sets up the electronic structure information from file fu40.
RPHAIT
Performs NINT-point Lagrangian interpolation of an asymptotic function used in
the electronic structure input file option (i.e., the RPH formulation).
RPHB
Calculates the curvature component of mode k.
RPHDXN
Converts from unweighted to mass-scaled gradient and normalizes the gradient
vector.
RPHEXP
Evaluates asymptotic exponential functional forms.
RPHFIT
Evaluates parameters of the asymptotic exponential fits.
RPHFT2
Computes 2-point fits to 3-parameter asymptotic exponential functions with the
range parameter fixed.
RPHFT3
Computes 3-point fits to 3-parameter asymptotic exponential functions.
RPHG1
Function used in the root search for the range parameter in an asymptotic
functional form.
RPHG2
Function used in the root search for the range parameter in an asymptotic
functional form.
RPHG5
Function used in the root search for the range parameter in an asymptotic
functional form.
RPHINT
Interpolates RPH information.
RPHMEF
Computes the effective tunneling mass for CD-SCSAG from the interpolated
value of the exponent in equation 19 in Ref. 48 in Sect. 21.
Polyrate 475
RPIVOT
Reads the Cartesian coordinates of pivot points
RPNT31
Reads the information from each point in the fu31 file.
RPHNWT
Performs a Newton search for the zero of one of the functions G(C) defined in
Subsection 9.D.1.
RPHRD1
Reads electronic structure input information and sets up tables used for
interpolation.
RPHRD2
Reads electronic structure input information.
RPHSET
Sets up electronic structure input interpolation information.
RPHTRF
Transforms the matrix of second derivatives with respect to unweighted
coordinates to second derivatives with respect to mass-scaled coordinates.
RPHTRX
Converts mass-scaled to Cartesian coordinates or Cartesian to mass-scaled
coordinates.
RPHWRT
Writes reaction path Hamiltonian interpolation information.
RPOTET
Reads the potential type.
RPOTGE
Reads the potential type to be used for optimizing the geometry.
RPRFL
Replaces the low-frequency mode of the stationary points when the IVTST0FREQ
keyword is used.
RPRMEP
Reads the parameters for printing the extra MEP information.
Polyrate 476
RPRVIB
Reads the range of s between which extra vibrational mode information and Qvib
are printed.
RPSEC40
Reads and processes a reactant or product section of the file fu40 input.
RQCOM
Calculates the distance between the centers of mass of two reacting species.
RQRST
Reads the information for the quantized-reactant-state tunneling calculation.
RQUAD
Reads the quadrature information for the tunneling calculations.
RRANGE
Reads the range of s values for which the reaction path is to be computed.
RRATE
Reads the RATE section of the file fu5 input.
RRPM
Reads the value of the RPM keyword of the file fu5.
RRSTRT
Reads the restart options.
RSCT
Reads the options for small curvature tunneling.
RSECND
Reads SECOND section of the file fu5 input.
RSFRST
Reads the variables for a special step size for the first n steps.
RSP
EISPACK diagonalization routine. Finds the eigenvalues and eigenvectors of a
real symmetric packed matrix.
RSPDRV
Accepts unpacked arrays the way EISPACK subroutine RS does, packs them for
RSPP, and calls RSPP to compute eigenvalues and eigenvectors.
Polyrate 477
RSPECL
Reads special values of s at which a normal mode analysis is to be done.
RSPP
Diagonalizes a real symmetric matrix in packed form.
RSSTOP
Reads the options of the SPECSTOP keyword.
RST
Diagonalizes a real symmetric matrix using RSPP.
RSTAT
Reads all the stationary point sections of the file fu5 input.
RSTATE
Reads the options used with a state-selected rate constant calculation.
RSVRC
Reads the range and step size of variable reaction coordinate
RTEMP
Reads the temperatures at which the rate constant is to be calculated.
RTITLE
Reads the title.
RTOR
Reads the TOR keyword options.
RTOROPT
Reads the TOROPT keyword options.
RTPJAC
Prints the MEP and large curvature representative tunneling termini in mass-
scaled Jacobian coordinates.
RTUNNL
Reads the tunneling parameters.
RUNM31
Reads the options for the IVTST-M interpolation on a unimolecular side (or side
with a well) on the reaction path.
Polyrate 478
RVAR6
Reads keyword values in a restart calculation.
RVARY
Reads the variable anharmonicity options desired for reactants, products and or
the saddle point.
RVPERT
Reads the options for using simple perturbation theory for the vibrational partition
functions.
RVRANG
Reads the anharmonicity options desired for the reaction path for specific regions
of the reaction coordinate s.
RVRCOPT
Reads the options for variable reaction coorindate calculations.
RWKB
Reads the WKB anharmonicity options.
RWORD
Parses a character string to find the next word.
RZVAR
Reads the z-matrix variables for the geometry optimization of the reactants,
products and the saddle point.
SADDLE
Computes the saddle point geometry (with subroutine NEWT) and other saddle
point properties.
SADENG
Computes the saddle point energetics.
Polyrate 479
SADSEC40
Reads and processes the SADDLE40 section of the file fu40 input.
SAVEXRP
Calculate Cartesian coordinate of each reactant and the other pivot points relative
to the first pivot point of reactant 1.
SECCEN
Calculates second derivatives by the method of central differences.
SECCEP
Calculates second derivatives by the method of central differences; only computes
part of the Hessian matrix.
SENOUT
Writes saddle point energetics information to unit fu6.
SETANH
Sets variables associated with the variable anharmonicity option.
SETLGS
Converts the variables and flags set by evaluating the keywords to the
corresponding LGS flags.
SETUP
Called once to initialize the potential, as discussed in Sect. 8.C.1. Ordinarily, this
is supplied by the user. The distribution, however, contains a dummy version for
use as described in Section 8.C, as well as sample versions for the test runs.
SETVAR
Converts the variables and flags set by evaluating the keywords to the
corresponding Polyrate variables.
SGND3V
Stores the sign of the third derivative in an array for use in computing the Morse
turning point.
SHFTSAD
Shifts saddle point information when using unit fu40 input.
SIGS
TSPACK subroutine that determines the value of the tension factors for a spline
under tension fit.
Polyrate 480
SIMPSN
Calculates the phase integral by using Simpson’s rule in the quantized-reactant-
state tunneling calculation.
SINE
Modified sine function.
SNHCSH
TSPACK subroutine that computes approximate values for modified hyperbolic
functions.
SORTG
Sorts frequencies in descending order.
SORT31
Sorts an nx2 array according to the values on the first column.
SPL1B1
Converts the spline fit data supplied by SPL1D1 to four arrays containing the
coefficients for local cubic fits.
SPL1B2
Computes the spline interpolation using the cubic polynomial coefficients
supplied by SPL1B1.
SPL1D1
Computes the second derivative array for spline interpolations.
SPL2D
Calls the 2D spline under tension.
SPL31
Subroutine that interfaces Polyrate and TSPACK. This subroutine is used when
the information is given by means of fu31, which allows for a different number of
data for each property.
SPLNB
Calculates the value of the curvature components at any point along the reaction
path by using spline under tension fitting.
SPLNF
Calculates the value of the frequencies at any point along the reaction path by
using spline under tension fitting.
SPLNM
Polyrate 481
Calculates the value of the moment of inertia at any point along the reaction path
by using spline under tension fitting.
SPLNMF
Calculates the value of the effective mass for CD-SCSAG tunneling at any point
along the reaction path by using spline under tension fitting.
SPLNV
Calculates the value of the energy along the reaction path, VMEP(s) at any point
along the reaction path by using spline under tension fitting.
SPLM31
Calculates the value of the moment of inertia at any point along the reaction path
by using spline under tension fitting. This subroutine is used when the input is
given in fu31.
SPLRMI
Calculates the value of the moment of inertia at any point along the reaction path
by using spline under tension fitting.
SPLSPV
Spline fits V in the ISPE method. This subroutine is used with fu51.
SPLV31
Calculates the value of the energy along the reaction path, VMEP(s), at any point
along the reaction path by using spline under tension fitting. This subroutine is
used when the input is given in fu31.
SSAVE
Saves the reaction path results calculated in subroutine PATH.
SSX
Computes the distance between two Cartesian geometries as an straight line in
mass-scaled coordinates.
STAT31
Calculates stationary point properties from the information read in fu5 and fu31.
STAUV
Calculates the correction term used in computing the improved generalized
transition-state partition function from the generalized transition-state partition
function.
Polyrate 482
STLGSJ
Converts the stationary-point-dependent variables and flags set by evaluating the
keywords to the corresponding LGS flags.
STOR
TSPACK subroutine that determines floating point number characteristics.
STVARJ
Converts the stationary-point-dependent variables and flags set by evaluating the
keywords to the corresponding Polyrate variables.
SURF
Evaluates the potential, as discussed in Subsection 8.C.1. Ordinarily this is
supplied by the user, but the Polyrate distribution provides a dummy version for
use as discussed in Section 8.C, as well as sample versions for the test runs.
SVBKSB
This routine, taken from Numerical Recipes, is for the backward substitution of
SV decomposition.
SVBCMP
This routine, taken from Numerical Recipes, is for the singular value
decomposition procedure.
TABLE
Writes a summary of selected forward rate constants to the file linked to
FORTRAN unit fu15.
TAUV
Calculates the cutoff partition function for improved canonical variational theory.
THETA2
Computes the phase integral for the semiclassical eigenvalues of a single-well
potential.
THETA3
Computes the phase integral for the semiclassical eigenvalues of a double-well
potential.
TITLE
Reads and writes the title of the job.
TP
Locates the turning points at a given energy for a normal mode vibration.
Polyrate 483
TPCDSC
Calculates the centrifugal-dominant small-curvature turning point.
TQL2
Computes the eigenvalues and eigenvectors of a symmetric tridiagonal matrix by
the QL method [H. Bowdler, R. S. Martin, C. H. Reinsch, and J. H. Wilkinson,
Num. Math 11 (1968) 293].
TQLRAT
Finds the eigenvalues of a symmetric tridiagonal matrix by the rational QL
method [C. H. Reinsch, Comm. ACM 16 (1973) 689].
TRANLF
Converts Cartesian to mass-weighted coordinates or mass-weighted to Cartesian
coordinates store in lower triangular form.
TRANS
Converts Cartesian to mass-scaled coordinates or mass-scaled to Cartesian
coordinates. Also converts derivatives of the potential energy function between
these coordinate systems.
TRANS2
Converts Cartesian to mass-scaled coordinates (IOP = 1) or mass-scaled to
Cartesian coordinates (IOP = 2) used in IVTST calculations.
TRANG
Transforms gradient in Cartesians to curvilinear internal coordinates.
TRANFC
Transforms Hessian in Cartesians to curvilinear internal coordinates.
TRANSF
Converts Cartesian to mass-weighted coordinates (IOP = 1) or mass-weighted to
Cartesian coordinates (IOP = 2).
TRBAK3
Forms the eigenvectors of a real symmetric matrix by back transformation of the
eigenvectors of the similar symmetric tridiagonal matrix.
TRED3
Reduces a real symmetric matrix to a symmetric tridiagonal matrix.
TREPT
Computes a parabolic fit, F = ax2+ bx + c, to three points.
TRLFRP
Polyrate 484
Stores the force constant matrix in lower triangle form.
TSC
Locates points where E = VaAG
and calculates the theta integral.
TSOUT
Computes and writes the final set of conventional transition state theory rate
constants. Also obtains activation energies and equilibrium constants.
TSPSI
TSPACK subroutine that computes a set of parameter values which define a
Hermite interpolatory tension spline.
TSRATE
Calculates the free energy of activation at the saddle point, individual reactant and
product partition functions, and conventional transition state theory rate constants
in the harmonic approximation. This routine is only used when the NOCVT
keyword is used in the RATE section. Some further discussion is provided in
Section 6.L of this manual.
TURNPT
Computes the concave-side turning point for the zero-point level in the
calculation of the curvature component.
UPCSE
Converts a line of characters to uppercase.
UPCAS
Converts lower case characters to upper case in the given string.
UPDHR
Updates the arrays FMIHR and FMIHTS in the VTST-IOC calculations.
UPDMI
Updates the arrays FMOM and FMITS in the VTST-IOC calculations.
VALVAG
Calculates the value of VaG for a given projected direction, given V, X, DX, and
F.
Polyrate 485
VECCON
Normalizes the normal mode vectors and converts them to mass-scaled
Cartesians.
VECMAG
Obtains the magnitudes of a set of vectors.
VICLCG
Calculates the classical energy corrections in the non-adiabatic region for the LCT
method in the VTST-IOC calculations.
VIVT
Computes the Eckart potential and its derivatives.
VPART
Computes the vibrational partition function.
VPARTI
Computes the vibrational partition function using the harmonic approximation.
VRCNEJ
Calculate number of available states for transitional modes using variable reaction
coorindate algorithm at canonical, microcanonical, and E,J -resolved
microcanonical levels.
VRCTST
Main subroutine to calculate reaction rate for loose transition state using variable
reaction coordinate and single-faceted or multifaceted dividing surface.
VSPLIN
Generates spline fits to the vibrationally adiabatic potential curve and the
effective reduced mass.
VSPLI2
Generates spline fits to the vibrationally adiabatic potential curve and the
effective reduced mass for IVTST calculations.
VTMUSN
Calculates the microcanonical variational sum of states in the calculation of the
microcanonical variational rate constant.
WTITLE
Writes the title of the run.
Polyrate 486
WKBENE
Calculates the energy eigenstates with the WKB approximation.
WKBPOT
Computes the energy levels of a quadratic-quartic function using a semiclassical
method with parabolic connection formulae.
WKBVIB
Driver for the calculation of WKB vibrational energies based on the true
(unfitted) potential for a given mode.
WRTHOK
Writes stationary point information to file fu61 and, if necessary, to file fu62.
WRTWEL
Writes the information about the wells to file fu6.
WVAR6
Writes the keyword values for a restart calculation.
XDOTP
Calculates the dot product of two vectors.
XERBLA
Error handler for the BLAS routines.
XPROD
Forms the cross product of vectors x and y, placing the result in vector z. All
vectors are of dimension three.
YDER24
Computes the second derivatives of the potential by fitting the analytic first
derivatives to a fourth-order polynomial around the desired location and then
taking the derivative of this polynomial. This is the hooks version of DERV24.
YDERV2
Calculates the Hessian matrix by using a quadratic fit to the potential energy
surface. Only the potential is used, not its first derivatives. This is the hooks
version of DERIV2.
YNEWT
Does a Newton-Raphson search for a stationary point. This is the hooks version
of NEWT.
Polyrate 487
YSECEN
Calculates second derivatives by the method of central differences. This is the
hooks version of SECCEN.
YSECEP
Calculates second derivatives by the method of central differences; only computes
part of the Hessian matrix. This is the hooks version of SECCEP.
YTRANS
Converts Cartesian coordinates to mass-scaled coordinates or converts mass-
scaled coordinates to Cartesian coordinates. Also converts derivatives of the
potential energy function between these coordinate systems. This is the hooks
version of TRANS.
ZEROPT
Computes the zero-point energy.
ZERP
Function that computes the zero-point energy.
ZIGAMA
Calculates the incomplete Gamma function of order 3/2.
ZOC3P
Prepares the correction information at 3 points for the VTST-IOC calculations.
ZOCAST
Checks the accuracy of the interpolation in the VTST-IOC calculations.
ZOCFRE
Calculates the corrections for the frequencies for VTST-IOC calculations.
ZOCPAR
Calculates the parameters for the VTST-IOC calculations.
ZOCPRN
Prints some of the information involved in VTST-IOC calculations.
ZOCUPD
Updates the arrays WER, FMOM, CDSCMU, VCLAS, WETS, and VADIB and
the variables EPRD and WSTAR with zero-order corrections for VTST-IOC
calculations.
ZOCVCL
Calculates the correction for the energy VMEP in VTST-IOC calculations.
Polyrate 488
ZRIDDR
Solves a nonlinear equation for calculating the range parameter of an Eckart
potential.
ZROUT
Explicitly initializes the work space for matrix with zeros to overcome the
FORTRAN save effect.
ZRPTE
Evaluates the zero-point energies.
ZSPMEP
Sets up information for ISPE. This subroutine is used with unit fu51.
17.A.2 User-supplied subprograms and module files
MODULE files:
aamod.f90
This FORTRAN 90 file contains all the modules used for passing
information between the various subprograms. It also contains all the
permanent constants for the Polyrate code. These parameters should not
be changed.
alloc.f90
This FORTRAN 90 file dynamically allocates memory for arrays according
to the user input file.
User-supplied subprograms:
SETUP
Subprogram supplied by the user that computes any necessary constants
for the potential (see Section 8 and examples in the test suite).
SURF
Subprogram supplied by the user that computes the potential and gradient
for a set of Cartesian coordinates (see Section 8 and examples in the test
suite).
17.A.3 FORTRAN files
acespoly.F
This file contains dummy subroutines used with ACESRATE.
Polyrate 489
energetics.F
This file contains subprograms for the calculations of properties of the PES.
These include subprograms that handle optimizations and numerical second
derivatives.
ef.F
This file contains the Eigenvector-Following algorithm for optimizing
geometries of the stationary points.
fromblas.F
This file contains all the subroutines from the BLAS math library.
givtst.F
This file contains subprograms for the global version of IVTST calculations.
headr.F
This file contains subprograms that print out the program header.
hooks.F
This file contains subprograms for interfacing electronic structure calculations
with POLYRATE.
intbsv1.F
This file contains subprograms for the transformations of the Cartesian
Hessians into a curvilinear coordinate system at non-stationary points along
the MEP and for the curvilinear coordinate vibrational analysis for linear and
nonlinear triatomics.
intbsv2.F
This file contains subprograms for the transformations of the Cartesian
Hessians into a curvilinear coordinate system at non-stationary points along
the MEP and for the curvilinear coordinate vibrational analysis for nonlinear
polyatomics. The coordinate transformation of the Hessian is based on the
transformation ANHTRAX program written by Matt Challacombe and Jerzy
Cioslowski.
intbsv3.F
This file contains subprograms for the transformations of Cartesian Hessians
into curvilinear coordinate system at reactants and products and for the
curvilinear coordinate vibrational analysis for nonlinear polyatomic.
interface.F
This file contains subprograms for parsing Polyrate keyword input.
Polyrate 490
ivtstm.F
This file contains subprograms for performing IVTST-M interpolation.
main.F
This file contains the driver for polyatomic VTST calculations.
main_vrcmpi.F
This file contains the driver for polyatomic VRC-TST calculations. It is a
substitution of main.F file.
mopoly.F
This file contains dummy subroutines used with MORATE.
polyag.F
This file contains subprograms with names beginning with letters A to G.
polyhl.F
This file contains subprograms with names beginning with letters H to L.
polymq.F
This file contains subprograms with names beginning with letters M to Q.
polyrr.F
This file contains subprograms with names beginning with the letter R.
polysz.F
This file contains subprograms with names beginning with letters S to Z.
poly31.F
This file contains subprograms that are used when POTENTIAL = unit31.
poly40.F This file contains subprograms that are used when POTENTIAL = unit40.
rtpjac.F
Polyrate 491
This file contains subprograms that are used to plot the MEP and large
curvature representative tunneling termini in mass-scaled Jacobian
coordinates.
vrctst_mpi.F
This file contains subprograms that are used to calculate reaction rate
for loose transition states using variable reaction coordinates and
single-faceted or multifaceted dividing surfaces. These subprograms
are parallelized using MPI.
17.B. Utility program detmi.f
In this version of POLYRATE, one of the VTST-IOC options [DETMI keyword] allows the
user to correct the calculated determinants of moment of inertia tensors with accurate
data. However, the values of determinants of moment of inertia tensors are not always
available in the literature or in the electronic structure calculation output of standard
codes. So, in this version of the Polyrate distribution we provide a small utility program,
detmi.f, in the util subdirectory of the POLYRATE17 directory. This program reads a
molecular geometry in Cartesians (in bohrs or in Angstroms) and the atomic weights (in
a.m.u.) of the constituent atoms of the molecule, and calculates the determinant of the
moment of inertia tensor of the molecule in all the units supported by the Polyrate unit
fu50 input options [UNITMI keyword]. (See subsection 12.F) The input formats are very
simple, and a detailed explanation can be found in the file detmi.doc in the same
subdirectory. A job control file detmi.jc and three sample input files, ch4.mi, ch4oh.mi,
and oh.mi are also provided.
One can use the compiling and linking commands listed in the Section 15 of this manual
to make an executable file detmi.exe for any machine. This program is easy to use;
however, one has to remember to do the following:
1. Make a data file. The program will read the data from a file called detmi.dat.
If your data file has a different name, copy, move, or link your file to this
name.
2. When finished, the program will generate an output file called detmi.out. It is
recommended that you move (or copy) this file to another file name before
doing any other calculations. Otherwise the new output will overwrite the old
detmi.out file, and the old information in that file will be lost.
Polyrate 492
3. There is a simple script detmi.jc in the same sub directory. It can do the above
file copying steps for you if you want. It takes the input file name as the only
argument.
For example, if your data file is called ch4.mi, type
detmi.jc ch4.mi <Return>
to do the calculation. The output will be written to the file detmi.out and copied to
the file ch4.out.
How to make an input data file:
1. In the first line you have to input three numbers in free format.
The first number is the number of atoms in the molecule.
The second number specifies if the geometry of the molecule is linear or
nonlinear. Set the number to 1 if it is linear. Set the number to 0 if the
geometry is not linear.
The third number specifies the input units for the Cartesians. Set it to 1 if the
units you use are Angstroms. Set the number to 0 if you use bohrs.
For example, if the target molecule is methane and your geometry data in
Cartesians are in Angstroms, the first line should look like the following:
5 0 1
2. The second and the third lines are the calculation titles. You can write whatever you
want here (less than 80 characters in one line).
For example:
Methane: CH4
QCISD/adj-cc-pVTZ geometry
3. The next n lines, where n is the first number you entered in the first line,
contains the atomic masses and Cartesian coordinate information. There
should be 4 numbers on each line. The first number is the atomic mass in
a.m.u. of the atom; the second, third, and fourth numbers are the x, y, and z
coordinates of the atom.
For example:
Polyrate 493
1.007825 0.0000 0.0000 0.0000
12.00000 1.0848 0.0000 0.0000
1.007825 1.4464 1.0228 0.0000
1.007825 1.4464 -0.5114 0.8857
1.007825 1.4464 -0.5114 -0.8857
17.C. Utility program hrotor.f
When some of the vibrational modes of the reactants, products, or GTS are treated as
hindered rotations, Polyrate allows the user to input more accurate values of the moments
of inertia of these modes in a VTST-IOC calculation [IC and HRMI keywords]. However,
usually the user can only get the geometry of a molecule and the vibrational eigenvectors
of these modes from an electronic structure calculation output.
The utility program hrotor.f is designed to take the atomic masses and geometry of the
molecule and the vibrational eigenvector of a hindered-rotor mode of the molecule and
then to calculate the moment of inertia using rectilinear model. It can also calculate the
harmonic, free rotor, and hindered rotor partition functions at different temperatures.
Detailed explanations can be found in the file hrotor.doc in the Polyrate17/util directory
and in Refs. 24, 29, and 30 in Sect. 21. A sample input file, cwmc.rmi, is also provided
in the Polyrate17/util directory.
You can use the compiling and linking commands listed in the Section 15 of this Polyrate
manual to make an executable file hrotor.exe for your machine. The program is designed
to read data from Unix standard input and write data to Unix standard output. To use the
program, type
hrotor.exe < input_file_name > output_file_name <Return>
For example:
hrotor.exe < cwmc.rmi > cwmc.rmi.out <Return>
Polyrate 494
To make a data file follow the steps below:
(Note: All the input data are in free format.)
1. In the first line you have to input 4 numbers.
The first number is the number of atoms in the molecule.
The second number specifies the units of the Cartesian coordinates you are
going to input. Set it to 0 if you use bohrs, to 1 if you use Angstroms.
The third number specifies the coordinate system of the vibrational
eigenvector you are going to input. Set it to 0 if you use a mass-scaled
coordinate system; set it to 1 if you use a non-mass-scaled Cartesian
coordinate system.
The fourth number specifies the number of temperatures at which you want to
calculate the partition function.
For example, if the target molecule is the saddle point of the reaction in the
Polyrate cwmctrl test run, your geometry data in Cartesians are in bohrs, the
eigenvector is in mass-scaled coordinates, and you want to calculate the
partition function at two temperatures, the first line should look like the
following:
9 0 0 2
2. The second and the third lines are the calculation titles. You can write
whatever you want here (less than 80 characters in one line).
For example:
Saddle point of the reaction in cwmc test run
The moment of inertia
3. If you set the third number in the first line to 1, skip this step. The next line is
the scaling mass in a.m.u. of the mass-scaled coordinate system which the
input eigenvector is based on.
For example:
1.0000
4. The next n lines, where n is the first number you entered in the first line,
contain the atomic masses of the constituent atoms in a.m.u.
Polyrate 495
For example:
12.00000
34.96885
1.007825
1.007825
1.007825
34.96885
1.007825
1.007825
15.99491
5. The next n lines, where n is the first number you entered in the first line,
contain the geometry data of the molecule in (unscaled) Cartesian coordinates.
There should be 3 numbers on each line, namely the x, y, and z coordinates of
the atom.
For example:
2.0187 -2.3695 0.1399
1.7442 -2.3695 4.4447
4.0466 -2.3695 0.1399
1.0334 -4.1335 0.1399
1.0334 -0.6054 0.1399
1.7442 -2.3695 -4.1650
-2.3564 -2.3695 1.5703
-2.3564 -2.3695 -1.2906
-3.4890 -2.3695 0.1399
6. The next n lines, where n is the first number you entered in the first line,
contain the vibrational eigenvector of this hindered-rotor mode. There should
be 3 numbers on each line, the x, y, and z components of the eigenvector for
the atom corresponding to this line.
For example:
0.000 0.567 0.000
0.000 -0.260 0.000
0.000 0.533 0.000
0.308 -0.008 0.000
-0.308 -0.008 0.000
0.000 -0.260 0.000
0.000 -0.116 0.000
0.000 -0.116 0.000
0.000 0.207 0.000
Polyrate 496
7. The next line contains the symmetry and subgroup information. The first
number is the symmetry factor of this hindered rotation. The second number is
the number of atoms in one of the subgroups. The next m numbers, where m is
the second number in this line, are the atom indices of those atoms in that
subgroup.
For example:
3 4 1 3 4 5
8. If you decide to calculate the partition function (i.e., if the fourth number in
the first line is greater than 0) you need to input the harmonic frequency in
cm-1 in a new line and the temperatures in Kelvin in the last line.
For example:
163.4794
600.00 1000.00
Polyrate 497
17.D. Utility programs findl.f and findb.f
In VTST-IOC calculations one has to input some range parameters for the correction
functions, in particular, the range parameter L for the Eckart function and the parameter B
for the cut-off Gaussian function on the reactant and/or product side. These parameters
are usually obtained by fitting a lower-level potential energy curve to the corresponding
functions. The utility programs findl.f and findb.f, which are located in the
Polyrate17/util subdirectory, are designed to do the fitting and return the optimized
values of L and B. The user can use the compiling and linking commands in Section 15 of
this Polyrate manual to make executable files (e.g., findl.exe and findb.exe). To use
these programs, just type the name of the executable file, and you will be prompted to
input the energies of 3 stationary points for findl.exe, or the energies of 2 stationary
points and the s value for one of the stationary points for findb.exe. Then, for both
programs, you will be prompted to input the energy and s value for another point along
the lower-level reaction path. This point is usually chosen to be the point that has an
energy halfway between the saddle point and the stationary point on the endothermic side
of the MEP for findl.exe or the reactant/product side stationary point for findb.exe. The
programs will then print the optimized value of L or B for the Eckart or cut-off Gaussian
function, respectively. The user can then use these values for the unit fu50 input
[RANGEIC keyword].
17.E. Utility program rotate30.f, rotate31.f, and rotate40.f
ROTATEx (x = 30, 31, or 40) is a FORTRAN program that uses as an input file a Polyrate
poly.fu30, poly.fu31, or poly.fu40 input file and orients the geometries on that file in a
consistent way along the reaction path. This program is based on the Chen orientation
algorithm Ref. 60 of Section 22.
The poly.fu30, poly.fu31, and poly.fu40 input files for Polyrate are usually constructed
from electronic structure calculations carried out by one of the several available
packages. These packages usually re-orient the input geometry in a way that allows the
program to take advantage of the symmetry of the system, or just to put the molecule in
the orientation preferred by the program. As a consequence, the input geometry is
oriented in a different way than the output geometry, gradients, and/or Hessians. This
results errors in: 1) reaction path following algorithms and 2) computation of reaction
Polyrate 498
path curvature. If we do not calculate the reaction path or the curvature of the reaction
path, the properties that Polyrate uses for the dynamical calculations are rotationally
invariant, and the results will not be affected by any rotation of any geometry. However,
if we want to calculate the reaction path curvature, we need to calculate the derivatives of
the Cartesian components of the gradient with respect to the reaction coordinate s. For
doing this, we require that all the points along the reaction path be oriented in the same
way. Otherwise, the numerical differentiation will lead to erroneous results.
The ROTATEx program uses a geometry that is input by the user (this is assumed to be the
saddle point geometry), and it reorients the first point along each side of the reaction path
according to this point. The following points along the reaction path are reoriented using
as reference geometry the previous point. This reorientation is done by means of the
Chen algorithm, as described in the original paper. However, this algorithm only works
for small rotations, so before applying Chen's method the program performs a series of
trial rotations in order to obtain the closest orientation to the reference geometry, and next
it applies Chen's method on the most similar orientation.
Chen's method is based on the minimization of the distance in mass-scaled Cartesian
coordinates of the two geometries. In some cases, this minimization does not converge.
When that happens, there is no way to solve the reorientation problem with this program.
The program can also recalculate the values of the reaction coordinate, s, as a straight line
between each pair of two consecutive points. This recalculation can be useful, e.g., for
calculating kinetic isotope effects.
There are three versions of the program ROTATEx: ROTATE30, ROTATE31, and ROTATE40,
and they are used for reorienting the geometries in poly.fu30, poly.fu31, and poly.fu40
input files, respectively. In order to perform this rotation it is necessary to
give the geometry of each point. This is sometimes not given on the poly.fu30 and
poly.fu40 input files. Thus, when we supply additional information on the gradients of
one or two points on each side of the Hessian points in poly.fu30 or poly.fu40, the
geometry of these one or two additional points per Hessian point is not given. This is the
reason why only poly.fu30 files with LOPT(6) = 2 will work with ROTATE30, and only
poly.fu40 input files with GRADER = NOEXTRA will work with ROTATE 40.
Polyrate 499
An additional limitation of the program is that it only works with poly.fu30 and poly.fu40
input files that do not include any anharmonic information.
Along with the source code, a test run is included for each program, as well as a sample
script for compiling and running the code.
The program requires two input files: (1) one of the Polyrate input files poly.fu30,
poly.fu31, or poly.fu40, and (2) a input file for the ROTATE program. The latter input file
is described next.
The first line of the input file consists of seven integers that indicate the number of atoms
in each system. The first integer is NATOM, the number of atoms in the saddle point
structure (which is assumed to be the same as the number of atoms for the points along
the reaction path) followed by six integers indicating the number of atoms in the first
reactant species, the second reactant, the first product, the second product, the reactants
well, and the products well, respectively. If one or more of these species don't exist, a
zero has to be input in its place.
The second line is a list of NATOM + 1 real numbers. The first one indicates the mass used
for scaling the Cartesian coordinates (which has to be the same as SCALEMASS in the
PATH section of the Polyrate poly.fu5 input file. The following NATOM real numbers are
the masses of each of the atoms present in the points along the reaction path, in the same
order as in in these points. All the masses have to be input in amu.
The third line is an integer that indicates if the values of s read from the poly.fu30,
poly.fu31, or poly.fu40 input files have to be kept unchanged or if the user wants to put in
their places the values computed by the program. If this integer is set to one, the values of
s that are read are discarded, and the calculated values are printed in the output file. Any
other value leads the program to preserve the s values that are input in the poly.fu30,
poly.fu31, or poly.fu40 input file.
The last information to be input in the ROTATE input file is the geometry in Cartesian
coordinates of the saddle point in atomic units. The three Cartesian coordinates for each
atom have to be preceded by an integer, which acts as a label. The ordering of the atoms
has to be the same as in the points along the reaction path, and the labels have to start
with the integer 1 for the first atom and finish with the integer NATOM for the last atom.
Polyrate 500
The output of the program, poly.fu60, is a file with the format same as poly.fu30,
poly.fu31, or poly.fu40, which can be used in a Polyrate calculation directly without
further modification.
17.F. Utility program SS-QRRK
The utility program directory SS-QRRK contains one .exe file, one source code file
(.f90), one directory for test runs, and one directory for outputs of test runs. SS-QRRK
code is a FORTRAN90 code for carrying out system-specific quantum RRK calculations.
Please refer to a separate manual for the use of SS-QRRK code.
Polyrate 501
18. UNIX C SHELL SCRIPTS AND PERL SCRIPTS
Polyrate includes many useful scripts for users. The following subsections discuss the
functions of these scripts and explain how to use them.
18.A. Installation script
This script, configure, resides in the Polyrate17 directory. It is used to install the Polyrate
program on your computer. Note that this installation is only for generating the Makefile,
and no executable is generated in this process. Usually, the first thing you do after
uncompressing and untarring the distribution tar file is to run this script. (See Subsection
15.A.) Actually, this script does four things:
1. Makes a hidden file .poly_path in your home directory.
The hidden file contains the path to the Polyrate17 directory in the file system you
are using. This lets other scripts in Polyrate easily locate the necessary files. If you
lose the hidden file for some reason, or if the file system changes after you install
POLYRATE, you need to run this script again to generate a new .poly_path file.
2. Asks the user to choose which kind of executable the user wants the Makefile to
generate: RP-VTST or VRC-VTST. (If you want both, you must run the script twice.)
3. Detects compilers, operating system, and processor type
The script will automatically search for the FORTRAN and C compilers that are
correct for the configuration being used.
4. Copies machine-dependent files and puts them into the proper directories with the
default file names.
It copies the appropriate date-and-time routine from the Polyrate17/util directory to
the Polyrate17/src directory and names it dattim.f.
If VRC-VTST installation is selected by the user, the script will install the SPRNG
2.0 library. If RP-VTST installation is chosen, the script will skip the SPRNG
installation step.
5. Creates the Makefile
Polyrate 502
The Makefile is used to compile and link all of the code needed for a job. If any
changes are made to the files used to create the executable, the Makefile will
automatically update the executable.
See section 15.A.1 for a description of the directory structure following a successful
installation.
18.B. Potential energy surface compiling scripts
This script is distributed in the current version, but it is no longer needed when using
Makefile.
There are two potential energy surface subroutine compiling scripts in the
Polyrate17/script directory. The script comp_pot.jc is used to compile all the potential
energy surface subroutines for the test runs. (See Subsection 15.A.2.)
The script potcomp.jc is designed to compile a single file of potential energy surface
subroutines. It is general, and you can use it to compile your own potential subroutines.
This script takes two arguments; the first one is the potential file name without extension,
and the second one is the number of atoms involved in the potential. For example,
suppose you have a set of FORTRAN potential energy subroutines which defines the
potential energy surface of a system that consists of one oxygen atom and 3 hydrogen
atoms, and the set of subroutines has the file name myoh3.f. Put this file in the
Polyrate17/poten directory. You then change to the Polyrate17/script directory and type
potcomp.jc myoh3 4 <Return>; the script will compile the file myoh3.f for you and put
the object module myoh3.o in the Polyrate17/obj directory. You can, if you wish, copy
the script into the Polyrate17/poten directory so you can use it more conveniently.
Remember that you must put your potential source code in the Polyrate17/poten
directory. It should be noted that since the nh3 potential energy surface subroutine
provided in the distribution package has already been written the way that is required by
POLYRATE, when compiling this potential energy subroutine with the script potcomp.jc,
you should use a number that is not 3 or 4 as the second argument. This is because the
nh3.f subprogram already contains the necessary SETUP, SURF, COORD, and CHAIN
subroutines.
Polyrate 503
18.C. Source code compiling script
This script is distributed in current, but it is no longer needed when using Makefile.
The script comp_src.jc in the script/ directory is used for compiling the Polyrate source
code. It takes one argument, the parameter INCLUDE file number. You probably used this
script when you did the testing. (See Subsection 15.A.2.) Usually, after you compile the
source code with a certain parameter INCLUDE file and keep the library file that the script
generated, you don't need to recompile the source code unless you need to use a different
parameter INCLUDE file. For example, suppose you write your own INCLUDE file named
param5.inc, and you want to compile the source code with this INCLUDE file. Put the
param5.inc file in the src/ directory, change to the script/ directory, and type comp_src.jc
5 & <Return>. The script will compile the source code with the parameter INCLUDE file
param5.inc and generate a library file named libpoly5.a in the obj/ directory. You can
then use the linking script described in the next subsection to link this library file with
your potential object module to make an executable file. Remember that you must put
the parameter INCLUDE file in the src/ directory and always name a new parameter file
param#.inc where # can be any integer greater than 4.
Polyrate 504
18.D. Linking script
This script is distributed in the current version, but it is no longer needed when using
Makefile.
The script link_exe.jc in the Polyrate17/script directory is used for linking the potential
object file with the source code library file to make an executable file. It takes 2
arguments. The first one is the library file number, which is just the parameter INCLUDE
file number you used when making the source code library file. (See the Subsection
above.) The second argument is the potential file name (without the extension) you want
to use. For example, if you want to use the source code library compiled with the
parameter file param5.inc and the potential object module myoh3.o to make an
executable file, change your working directory to the script/ directory and type
link_exe.jc 5 myoh3 <Return>. The script will link the source code library and potential
object files together and generate the executable file poly_myoh3.exe and a short
summary file poly_myoh3.doc about this new executable file in the exe/ directory.
18.E. Test run scripts
The test run scripts have been discussed in Subsection 15.A.2. These scripts are designed
such that you don't need to know much about Polyrate in order to run the test runs. Some
of the test runs might take a long time to run (see Sect. 21) so you should consider
running them in background or submitting them as batch jobs. Some test runs generate
very big output files that you may want to delete together with the test run executable
files when you need to free up some disk space.
Polyrate 505
19. FILE USAGE
The Polyrate program uses several files for input data, for storing restart information
(optional), and for output. The program explicitly opens and closes all files required for a
given run, and the files are assumed to have the file names poly.fu#, where # is an
integer. The file poly.fu# connects to a FORTRAN I/O unit fu# which is defined in the
file aamod.f90 (see Subsection 5.A). This means that at the beginning of any run, all the
Polyrate input data files which have logical file names differing from poly.fu# must be
linked or copied to the corresponding poly.fu# file. If the user wishes to assign different
logical names to the output files, which are also poly.fu# files, these reassignments must
be carried out after the calculation has completed. Any data file(s) needed by the
potential energy surface subroutine is (are) not opened by the Polyrate program and
therefore, do not automatically follow the poly.fu# format.
One would ordinarily expect FORTRAN unit 5 to be assigned to fu5, FORTRAN unit 6
to fu6, and so forth. The fu# system, however, allows one to avoid conflicts when
hooking Polyrate up to other programs, e.g., MOPAC or analytic potentials.
Unit Usage
fu1 Reaction-path information for restarting the program
fu2 Additional reaction-path information to be merged with that
from unit fu1
fu3 Output for merged reaction path information
fu4 Reserved for potential energy surface data
(Note: A potential subroutine may read data from more than
one file, if desired. In the test suite we always use unit 4 if data
is read from only one file, and we use units 4 and 7 for the
cases where data is read from two files)
fu5 General input data. This data has several sections—see section
12.A of this manual for the details.
fu6 Output (This is the full output file. Selected subsets of this
output are also written to files poly.fu14 and poly.fu15)
fu7 Usually reserved for additional potential energy surface data
(See Subsections 8.C and 16.B for further discussion)
Polyrate 506
fu14 Output table of dynamical bottleneck properties
fu15 Output table of selected forward rate constants
fu16 Reserved for output from electronic structure packages
fu22 Detailed output for the LCT calculations [LCTOPT: PRFREQ,
PRPROB]
fu24 Output file of MEP and large curvature representative tunneling
termini in mass-scaled Jacobian coordinates.
fu25 Output file of the potential energy information along the MEP
fu26 Output file of the generalized transition state frequency
information along the MEP
fu27 Generalized transition state geometry information along the
MEP in the XYZ input format of the XMOL program
fu28 Bond angles, bond distances, and dihedral angles along the
MEP
fu29 Electronic structure input file for IVTST-0 and IVTST-1
calculations
fu30 Formatted electronic structure input file used if POTENTIAL =
unit 30 in the ENERGETICS Section of file fu5
fu31 Keyword-based electronic structure input file used if POTENTIAL = unit31 in the ENERGETICS section of file fu5.
fu40 Keyword-based electronic structure input file used if
POTENTIAL = unit40 in the ENERGETICS section of file fu5
fu41–fu47 Output tables of LCT calculations [LCTDETAIL]
fu48,fu49 Output files for LCT restart calculations
fu50 Input file for higher-level data for VTST-IOC calculations [DL
keyword set to ioc or ICOPT]
fu51 Input file for higher-level data for VTST-ISPE calculations [DL keyword set to ispe]
Polyrate 507
fu60 Reserved for the direct dynamics intermediate file
fu61 Reserved for information about stationary points that can be
used to restart a calculation by the second restart method of
Section 7. C.
fu62 Reserved for a subset of information that are presented in fu61
if the argument of the WRITE62 keyword is not set to none
fu65 Generalized transition state geometry information along the
MEP in the XYZ input format of the MDMOVIE program
fu70 Reserved for input data needed by PREP
fu71 Reserved for input data needed by PREPJ when JTYPE = 1
(REACT1)
fu72 Reserved for input data needed by PREPJ when JTYPE = 2
(REACT2)
fu73 Reserved for input data needed by PREPJ when JTYPE = 3
(PROD1)
fu74 Reserved for input data needed by PREPJ when JTYPE = 4
(PROD2)
fu75 Reserved for input data needed by PREPJ when JTYPE = 5
(START)
fu76 Reserved for input data needed by PREPJ when JTYPE = 6
(PATH)
fu77 Reserved for input data needed by PREPJ when JTYPE = 7
(WELLR)
fu78 Reserved for input data needed by PREPJ when JTYPE = 8
(WELLP)
fu80-fu89 Reserved for electronic structure codes and interfaces
Polyrate 508
20. CITATIONS INDICATED BY BRACKETS IN THE TEXT
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Polyrate 509
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Polyrate 510
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[63] J. Zheng and D. G. Truhlar, Faraday Discuss. 157 (2012) 59.
[64] J. Zheng, S. L Mielke, K. L Clarkson, and D. G. Truhlar, Computer Phys.
Commun. 183 (2012) 1803.
[65] J. Zheng, R. Meana-Pañeda, and D. G. Truhlar, Computer Phys. Commun.184
(2013) 2032.
[66] J. Zheng, S. L Mielke, K. L Clarkson, R. Meana-Pañeda, and D. G. Truhlar,
MSTOR, (University of Minnesota, Minneapolis, 2014).
http://comp.chem.umn.edu/mstor
[67] A. Fernández-Ramos, B. A. Ellingson, R. Meana-Pañeda, J. M. C. Marques, and
D. G. Truhlar, Theor. Chem. Acc. 118 (2007) 813.
[68] J. Zheng and D. G. Truhlar, J. Chem. Theory Comput. 9 (2013) 2875.
[69] I. M. Alecu, J. Zheng, Y. Zhao, and D. G. Truhlar, J. Chem. Theory Comput. 6
(2010) 2872.
[70] J. Zheng, T. Yu, E. Papajak, I, M. Alecu, S. L. Mielke, and D. G. Truhlar, Phys.
Chem. Chem. Phys. 13 (2011) 10885.
[71] J. Zheng and D. G. Truhlar, J. Chem. Theory Comput. 9 (2013) 1356.
[72] J. L. Bao, R. Meana-Pañeda, and D. G. Truhlar, Chem. Sci. 6 (2015), 5866.
[73] J. L. Bao, J. Zheng, and D. G. Truhlar, J. Am. Chem. Soc. 138 (2016), 2690.
[74] J. L. Bao, X. Zhang, and D. G. Truhlar, Phys. Chem. Chem. Phys. 18 (2016),
16659.
Polyrate 511
[75] “Barrierless association of CF2 and dissociation of C2F4 by variational transition
state theory and system-specific quantum Rice–Ramsperger–Kassel theory,” J. L.
Bao, X. Zhang, and D. G. Truhlar, Proceedings of the National Academy of
Sciences, U.S.A., 113, (2016), 13606.
Polyrate 512
21. BIBLIOGRAPHY
Note : See Sect. 20 for references indicated by brackets in the text of the manual.
The following is a list of some publications reporting calculations carried out with
Polyrate or with its very much older version, which was entitled ICVTST. This includes
all articles in which new procedures incorporated in Polyrate are described, but it does
not include all applications.
1. “Polyatomic Canonical Variational Theory for Chemical Reaction Rates. Separable-
Mode Formalism with Application to OH + H2 → H2O + H”, A. D. Isaacson and D.
G. Truhlar, J. Chem. Phys. 76, 1380 (1982).
2. “The Incorporation of Quantum Effects in Generalized Transition State Theory”, D.
G. Truhlar, A. D. Isaacson, R. T. Skodje, and B. C. Garrett, J. Phys. Chem . 86, 2252
(1982); erratum: 87, 4554 (1983).
3. “Statistical-Diabatic Model for State-Selected Reaction Rates. Theory and
Application of Vibrational-Mode Correlation Analysis to OH(nOH) + H2(nHH) →
H2O + H”, D. G. Truhlar and A. D. Isaacson, J. Chem. Phys. 77, 3516 (1982).
4. “Variational Transition State Theory Calculations for an Atom-Radical Reaction
with no Saddle Point: O + OH”, S. N. Rai and D. G. Truhlar, J. Chem. Phys. 79,
6049 (1983).
5. “Generalized Transition State Theory”, D. G. Truhlar, A. D. Isaacson, and B. C.
Garrett, in The Theory of Chemical Reaction Dynamics, edited by M. Baer (CRC
Press, Boca Raton, FL, 1985), Vol. 4, pp. 65-137.
6. “Improved Canonical and Microcanonical Variational Transition State Theory
Calculations for a Polyatomic System: OH + H2 → H2O + H”, A. D. Isaacson, M.
T. Sund, S. N. Rai, and D. G. Truhlar, J. Chem. Phys. 82, 1338 (1985).
7. “Semiclassical Reaction-Path Methods Applied to Calculate the Tunneling Splitting in NH3”, F. B. Brown, S. C. Tucker, and D. G. Truhlar, J. Chem. Phys. 83, 4451
(1985).
8. “Diffusion of Hydrogen, Deuterium, and Tritium on the (100) Plane of Copper:
Reaction-Path Formulation, Variational Transition State Theory and Tunneling
Calculations”, J. G. Lauderdale and D. G. Truhlar, Surface Science 164, 558
(1985).
9. “Embedded-Cluster Model for the Effect of Phonons on Hydrogen Surface
Diffusion on Copper”, J. G. Lauderdale and D. G. Truhlar, J. Chem. Phys. 84, 1843
(1986).
10. “Test of Variational Transition State Theory and the Least-Action Approximation
for Multidimensional Tunneling Probabilities Against Accurate Quantal Rate
Constants for a Collinear Reaction Involving Tunneling into an Excited State”, B.
C. Garrett, N. Abusalbi, D. J. Kouri, and D. G. Truhlar, J. Chem. Phys. 83, 2252
(1985).
Polyrate 513
11. “The Representation and Use of Potential Energy Surfaces in the Wide Vicinity of a
Reaction Path for Dynamics Calculations on Polyatomic Reactions”, D. G. Truhlar,
F. B. Brown, R. Steckler, and A. D. Isaacson, in The Theory of Chemical Reaction
Dynamics, edited by D. C. Clary (D. Reidel, Dordrecht, Holland, 1986), pp. 285.
12. “Semiclassical Variational Transition State Calculations for the Reactions of H and D with Thermal and Vibrationally Excited H2”, B. C. Garrett, D. G. Truhlar, A. J.
C. Varandas, and N. C. Blais, International J. Chem. Kinetics 18, 1065 (1986).
12A. “Evaluation of Dynamical Approximations for Calculating the Effect of Vibrational
Excitation on Reaction Rates”, B. C. Garrett, D. G. Truhlar, J. M. Bowman, and AF
Wagner, J. Phys. Chem. 90, 4305 (1986).
13. “Reaction-Path Analysis of the Tunneling Splitting in Fluxional Molecules:
Application to the Degenerate Rearrangement of Hydrogen Fluoride Dimer”, G. C.
Hancock, P. A. Rejto, R. Steckler, F. B. Brown, D. W. Schwenke, and D. G.
Truhlar, J. Chem. Phys. 85, 4997 (1986).
14. “POLYRATE: A General Computer Program for Variational Transition State Theory
and Semiclassical Tunneling Calculations of Chemical Reaction Rates”, A. D.
Isaacson, D. G. Truhlar, S. N. Rai, R. Steckler, G. C. Hancock, B. C. Garrett, and
M. J. Redmon, Comp. Phys. Comm. 47, 91 (1987).
15. “Surface Diffusion of H on Copper: The Effect of Phonon-Adsorbate Coupling on
the Diffusion Rate”, T. N. Truong and D. G. Truhlar, J. Phys. Chem. 91, 6229
(1987).
16. “A Comparative Study of Potential Energy Surfaces for CH3 + H2→ CH4 + H”, R.
Steckler, K. Dykema, F. B. Brown, D. G. Truhlar, and T. Valencich, J. Chem. Phys.
87, 7024 (1987).
17. “A New Potential Energy Surface for the CH3 + H2 → CH4 + H Reaction:
Calibration, Rate Constants, and Kinetic Isotope Effects by Variational Transition
State Theory and Semiclassical Tunneling Calculations”, T. Joseph, R. Steckler,
and D. G. Truhlar, J. Chem. Phys. 87, 7036 (1987).
18. “Algorithms and Accuracy Requirements for Computing Reaction Paths by the
Method of Steepest Descent”, B. C. Garrett, M. J. Redmon, R. Steckler, D. G.
Truhlar, M. S. Gordon, K. K. Baldridge, and D. Bartol, J. Phys. Chem. 92, 1476
(1988).
19. “Calculation of Reaction Rates and Kinetic Isotope Effects for Dissociative Chemisorption of H2 and D2 on Ni(100), Ni(110) and Ni(111) Surfaces”, T. N.
Truong, G. Hancock, and D. G. Truhlar, Surface Science 214, 523 (1989).
20. “Ab Initio Reaction Paths and Direct Dynamics Calculations”, K. K. Baldridge, M.
S. Gordon, R. Steckler, and D. G. Truhlar, J. Phys. Chem. 93, 5107 (1989).
21. “Application of the Large-Curvature Tunneling Approximation to Polyatomic
Molecules: Abstraction of H or D by Methyl Radical”, B. C. Garrett, T. Joseph, T.
N. Truong, and D. G. Truhlar, Chem. Phys. 136, 271 (1989); erratum: 140, 207
(1990).
Polyrate 514
22. “Transition State Structure, Barrier Height, and Vibrational Frequencies for the
Reaction Cl + CH4 → CH3 + HCl”, T. N. Truong, D. G. Truhlar, K. K. Baldridge,
M. S. Gordon, and R. Steckler, J. Chem. Phys. 90, 7137 (1989).
23. “Projection Operator Method for Geometry Optimization with Constraints”, D.-h.
Lu, M. Zhao, and D. G. Truhlar, J. Comp. Chem. 12, 376 (1991).
24. “A Simple Approximation for the Vibrational Partition Function of a Hindered
Internal Rotation”, D. G. Truhlar, J. Comp. Chem. 12, 266 (1991).
25. “The Definition of Reaction Coordinates for Reaction-Path Dynamics”, G. A.
Natanson, B. C. Garrett, T. N. Truong, T. Joseph, and D. G. Truhlar,
J. Chem. Phys. 94, 7875 (1991).
26. “Interpolated Variational Transition State Theory: Practical Methods for Estimating
Variational Transition State Properties and Tunneling Contributions to Chemical
Reaction Rates from Electronic Structure Calculations”, A. Gonzalez-Lafont, T. N.
Truong, and D. G. Truhlar, J. Chem. Phys. 95, 8875 (1991).
27. “Optimized Calculation of Reaction Paths and Reaction-Path Functions for
Chemical Reactions”, V. S. Melissas, D. G. Truhlar, and B. C. Garrett, J. Chem.
Phys. 96, 5758 (1992).
28. “Variational Transition-State Theory with Multidimensional, Semiclassical,
Ground-State Transmission Coefficients: Application to Secondary Deuterium
Kinetic Isotope Effects in Reactions Involving Methane and Chloromethane”, D. G.
Truhlar, D.-h. Lu, S. C. Tucker, X. G. Zhao, A. Gonzàlez-Lafont, T. N. Truong, D.
Maurice, Y-.P. Liu, and G. C. Lynch, ACS Symp. Series 502, 16 (1992).
29. “Polyrate 4: A New Version of a Computer Program for the Calculation of
Chemical Reaction Rates for Polyatomics”, D.-h. Lu, T. N. Truong, V. S. Melissas,
G. C. Lynch, Y.-P. Liu, B. C. Garrett, R. Steckler, A. D. Isaacson, S. N. Rai, G.
Hancock, J. G. Lauderdale, T. Joseph, and D. G. Truhlar, Comp. Phys. Comm. 71,
235 (1992).
30. “MORATE: A Program for Direct Dynamics Calculations of Chemical Reaction
Rates by Semiempirical Molecular Orbital Theory”, T. N. Truong, D.-h. Lu, G. C.
Lynch, Y.-P. Liu, V. S. Melissas, J. J. P. Stewart, R. Steckler, B. C. Garrett, A. D.
Isaacson, A. Gonzalez-Lafont, S. N. Rai, G. C. Hancock, T. Joseph, and D. G.
Truhlar, Comp. Phys. Comm. 75, 143 (1993).
31. “Molecular Modeling of the Kinetic Isotope Effect for the [1,5]-Sigmatropic
Rearrangement of cis-1,3-Pentadiene”, Y.-P. Liu, G. C. Lynch, T. N. Truong, D.-h.
Lu, and D. G. Truhlar, J. Amer. Chem. Soc. 115, 2408 (1993).
32. “Interpolated Variational Transition State Theory and Tunneling Calculations of the
Rate Constant of the Reaction OH + CH4 at 223-2400 K”, V. S. Melissas and D. G.
Truhlar, J. Chem. Phys. 99, 1013 (1993).
33. “Bond-Distance and Bond-Angle Constraints in Reaction-Path Dynamics
Calculations”, D.-h. Lu and D. G. Truhlar, J. Chem. Phys. 99, 2723 (1993).
Polyrate 515
34. “Direct Dynamics Calculation of the Kinetic Isotope Effect for an Organic
Hydrogen-Transfer Reaction, Including Corner-Cutting Tunneling in 21
Dimensions”, Y.-P. Liu, D.-h. Lu, A. Gonzalez-Lafont, D. G. Truhlar, and B. C.
Garrett, J. Amer. Chem. Soc. 115, 7806 (1993).
35. “Effect of Phonon Coupling on Hydrogen Tunneling Rates at Gas-Surface
Interfaces”, S. E. Wonchoba and D. G. Truhlar, J. Chem. Phys. 99, 9637 (1993).
36. “Variational Transition State Theory and Semiclassical Tunneling Calculations with
Interpolated Corrections: A New Approach to Interfacing Electronic Structure
Theory and Dynamics for Organic Reactions”, W.-P. Hu, Y.-P. Liu, and D. G.
Truhlar, Faraday Trans. Chem. Soc. 90, 1715 (1994).
37. “Reaction Path Approaches to Dynamics at a Gas-Solid Interface: Quantum
Tunneling Effects for an Adatom on a Non-Rigid Metallic Surface”, S. E.
Wonchoba, W.-P. Hu, and D. G. Truhlar in Theoretical and Computational
Approaches to Interface Phenomena, edited by H. L. Sellers and J. T. Golab
(Plenum, New York, 1994), p. 1.
38. “Surface Diffusion of H on Ni(100). Interpretation of the Transition Temperature”,
S. E. Wonchoba, W.-P. Hu, and D. G. Truhlar, Phys. Rev. B 51, 9985 (1995).
39. “Polyrate 6.5: A New Version of Computer Program for the Calculation of
Chemical Reaction Rates for Polyatomics”, R. Steckler, W.-P. Hu, Y.-P. Liu, G. C.
Lynch, B. C. Garrett, A. D. Isaacson, V. S. Melissas, D.-h. Lu, T. N. Truong, S. N.
Rai, G. C. Hancock, J. G. Lauderdale, T. Joseph, and D. G. Truhlar, Computer
Physics Communications 88, 341 (1995).
40. “Direct Dynamics Method for the Calculation of Reaction Rates”, D. G. Truhlar, in
The Reaction Path in Chemistry: Current Approaches and Perspectives, edited by
D. Heidrich (Kluwer, Dordrecht, 1995), p. 229.
41. “Reaction-Path Potential and Vibrational Frequencies in Terms of Curvilinear
Internal Coordinates”, C. F. Jackels, Zhen Gu, and D. G. Truhlar, J. Chem. Phys.
102, 3188 (1995).
42. “Dual-Level Reaction Path Dynamics (The /// Approach to VTST with
Semiclassical Tunneling). Application to OH + NH3 → H2O + NH2 “ J.C.
Corchado, J. Espinosa-Garcia, W.-P. Wu, I. Rossi, and D. G. Truhlar, J. Phys.
Chem. 99, 687 (1995).
43. “Reaction-Path Dynamics in Curvilinear Internal Coordinates Including Torsions,”
K. A. Nguyen, C. F. Jackels, and D. G. Truhlar, J. Chem. Phys. 104, 6491 (1996).
44. “Improved Dual-Level Direct Dynamics Method for Reaction Rate Calculations
with Inclusion of Multidimensional Tunneling Effects and Validation for the Reaction of H with trans-N2H2” Y.-Y. Chuang, and D. G. Truhlar, J. Phys. Chem.
A 101, 3808 (1997); erratum: 101, 8741 (1997).
45. “Reaction-Path Dynamics with Harmonic Vibrational Frequencies in Curvilinear
Internal Coordinates: H + trans-N2H2 → H2 + N2H”, Y.-Y. Chuang and D. G.
Truhlar, J. Chem. Phys. 107, 83 (1997).
46. “Reaction Path Dynamics in Redundant Internal Coordinates,” Y.-Y. Chuang and
D. G. Truhlar, J. Phys. Chem. A 102, 242 (1998).
Polyrate 516
47. “Variation Transition State Theory Without the Minimum-Energy Path,” J. Villà
and D. G. Truhlar, Theor. Chem. Acc. 97, 317 (1997).
48. “Mapped Interpolation Methods for Variational Transition State Theory,” J. C.
Corchado, E. L. Coitiño, Y.-Y. Chuang, P. L. Fast, D. G. Truhlar, J. Phys. Chem. A
102, 2424 (1998).
49. “Variational Reaction Path Algorithm,” P. L. Fast and D. G. Truhlar, J. Chem.
Phys. 109, 3721 (1998).
50. “The Calculation of Kinetic Isotope Effects Based on a Single Reaction Path,” P. L.
Fast, J. C. Corchado, and D. G. Truhlar, J. Chem. Phys. 109, 6237 (1998).
51. “Interface of Electronic Structure and Dynamics for Reactions in Solution,” Y.-Y.
Chuang, C. J. Cramer, and D. G. Truhlar, International Journal of Quantum
Chemistry 70, 887-896 (1998). (Sanibel issue) doi.org/10.1002/(SICI)1097-461X(1998)70:4/5<887::AID-QUA34>3.0.CO;2-W
52. “Mapped Interpolation Scheme for Single-Point Energy Corrections in Reaction
Rate Calculations and a Critical Evaluation of Dual-Level Reaction-Path Dynamics
Methods,” Y.-Y. Chuang, J. C. Corchado, and D. G. Truhlar, J. Phys. Chem. A 103,
1140 (1999).
53. “Statistical Thermodynamics of Bond Torsional Modes”, Y.-Y. Chuang and D. G.
Truhlar, J. Chem. Phys. 112, 1221 (2000); 121, 7036(E) (2004); 124, 0000(E)
(2006).
54. “Nonequilibrium Solvation Effects for a Polyatomic Reaction in Solution”, Y.-Y.
Chuang and D. G. Truhlar, J. Amer. Chem. Soc., 121, 10157 (1999).
55. “Improved Algorithm for Corner Cutting Calculations”, A. Fernandez-Ramos and
D. G. Truhlar, J. Chem. Phys. 114, 1491 (2001).
56. “Interpolated Algorithm for Large-Curvature Tunneling Calculations of
Transmission Coefficients for Variational Transition State Theory Calculations of
Reaction Rates”, A. Fernandez-Ramos, D. G. Truhlar, J. C. Corchado, and J.
Espinosa-Garcia, J. Phys. Chem. A 106, 4957 (2002).
57. "Tests of Potential Energy Surfaces for H + CH4 <-> CH3 + H2: Deuterium and
Muonium Kinetic Isotope Effects for the Forward and Reverse Reaction," J. Pu and
D. G. Truhlar, J. Chem. Phys. 117, 10675-10687 (2002).
58. "Efficient Molecular Mechanics for Chemical Reactions: Multiconfiguration
Molecular Mechanics using Partial Electronic Structure Hessians," H. Lin, J. Pu, T.
V. Albu, and D. G. Truhlar, J. Phys. Chem. A 108, 4112-4124 (2004).
59. "Temperature Dependence of Carbon-13 Kinetic Isotope Effects of Importance to
Global Climate Change," H. Lin, Y. Zhao, B. A. Ellingson, J. Pu, and D. G.
Truhlar, Journal of the American Chemical Society 127, 2830-2831 (2005).
60. "A New Algorithm for Efficient Direct Dynamics Calculations of Large- Curvature
Tunneling and Its Application to Radical Reactions with 9-15 Atoms," A.
Fernández-Ramos and D. G. Truhlar, Journal of Chemical Theory and Computation
1, 1063-1078 (2005).
Polyrate 517
61. "Variational Transition State Theory," B. C. Garrett and D. G. Truhlar, in Theory
and Applications of Computational Chemistry: The First Forty Years, edited by C.
E. Dykstra, G. Frenking, K. S. Kim, and G. E. Scuseria (Elsevier, Amsterdam,
2005), pp. 67-87.
62. "Variational Transition State Theory and Multidimensional Tunneling for Simple
and Complex Reactions in the Gas Phase, Solids, Liquids, and Enzymes," D. G.
Truhlar, in Isotope Effects in Chemistry and Biology, edited by A. Kohen and H.-H.
Limbach (Marcel Dekker, Inc., New York, 2006), pp. 579-
620.http://t1.chem.umn.edu/Truhlar/docs/C71.pdf
63. "Statistical Thermodynamics of Bond Torsional Modes. Tests of Separable,
Almost-Separable and Improved Pitzer-Gwinn Approximations", B. A. Ellingson,
V. A. Lynch, S. L. Mielke, and D. G. Truhlar, Journal of Chemical Physics 125,
084305/1-17 (2006).
64. "Multidimensional Tunneling, Recrossing, and the Transmission Coefficient for
Enzymatic Reactions,” J. Pu, J. Gao, and D. G. Truhlar, Chemical Reviews 106,
3140-3169 (2006).
65. "Multi-Configuration Molecular Mechanics Based on Combined Quantum
Mechanical and Molecular Mechanical Calculations," H. Lin, Y. Zhao, O.
Tishchenko, and D. G. Truhlar, Journal of Chemical Theory and Computation 2,
1237-1254 (2006).
66. "Optimizing the Performance of the Multiconfiguration Molecular Mechanics
Method," O. Tishchenko and D. G. Truhlar, Journal of Physical Chemistry A 110,
13530-13536 (2006).
67. "Transition State Theory and Chemical Reaction Dynamics in Solution," D. G.
Truhlar and J. R. Pliego Jr., in Continuum Solvation Models in Chemical Physics:
Theory and Application, edited by B. Mennucci and R. Cammi (Wiley), submitted
Oct. 6, 2006.
68. "Modeling of Bimolecular Reactions," A. Fernández-Ramos, J. A. Miller, S. J.
Klippenstein, and D. G. Truhlar, Chemical Reviews 106, 4518-4584 (2006).
69. "Variational Transition State Theory in the Treatment of Hydrogen Transfer
Reactions, " D. G. Truhlar and B. C. Garrett, in Hydrogen Transfer Reactions,
edited by J. T. Hynes, J. P. Klinman, H. H. Limbach, and R. L. Schowen (Wiley-
VCH, Weinheim, Germany, 2007), Vol. 2, pp. 833-874.
70. "Hydrogen Atom Transfers in B12 Enzymes," R. Banerjee, D. G. Truhlar, A.
Dybala-Defratyka, P. Paneth, in Hydrogen Transfer Reactions, edited by J. T.
Hynes, J. P. Klinman, H.-H. Limbach, and R. L. Schowen (Wiley-VCH, Weinheim,
Germany, 2007), Vol. 4, pp. 1473-1495.
71. "Variational Transition State Theory with Multidimensional Tunneling," A.
Fernandez-Ramos, B. A. Ellingson, B. C. Garrett, and D. G. Truhlar, in Reviews in
Computational Chemistry, Vol. 23, edited by K. B. Lipkowitz and T. R. Cundari
(Wiley-VCH, Hoboken, NJ, 2007), pp. 125-232.
Polyrate 518
72. "Global Potential Energy Surfaces with Correct Permutation Symmetry by Multi-
Configuration Molecular Mechanics," O. Tishchenko and D. G. Truhlar, Journal of
Chemical Theory and Computation 3, 938-948 (2007). doi.org/10.1021/ct600315h
73. "Symmetry Numbers and Chemical Reaction Rates," A. Fernández-Ramos, B. A.
Ellingson, R. Meana-Pañeda, J. M. C. Marques and D. G. Truhlar, Theoretical
Chemistry Accounts 118, 813-826 (2007). doi.org/10.1007/s00214-007-0328-0
74. "Multi-Coefficient Gaussian-3 Calculation of the Rate Constant for the OH + CH4
Reaction and its 12C/13C Kinetic Isotope Effect with Emphasis on the Effects of
Coordinate System and Torsional Treatment," B. A. Ellingson, J. Pu, H. Lin, Y.
Zhao, and D. G. Truhlar, Journal of Physical Chemistry A 111, 11706-11717
(2007). doi.org/10.1021/jp072843j
75. "Explanation of the Unusual Temperature Dependence of the Atmospherically
Important OH + H2S → H2O + SH Reaction and Prediction of the Rate Constant at
Combustion Temperatures," B. A. Ellingson, and D. G. Truhlar, Journal of the
American Chemical Society 129, 12765-12771 (2007). doi.org/10.1021/ja072538b
76. "Reactions of Hydrogen Atom with Hydrogen Peroxide," B. A. Ellingson, D. P.
Theis, O. Tishchenko, J. Zheng, and D. G. Truhlar, J. Phys. Chem. A 111, 13554-
13566 (2007). doi.org/10.1021/jp077379x
77. "Density Functional Study of Methyl Radical Association Reaction Kinetics," J.
Zheng, S. Zhang, and D. G. Truhlar, Journal of Physical Chemistry A 112, 11509-
11513 (2008). dx.doi.org/10.1021/jp806617m
78. "Mechanistic Analysis of the Base-Catalyzed HF Elimination from 4-Fluoro-4-(4'-
nitrophenyl)butane-2-one Based on Liquid-Phase Kinetic Isotope Effects Calculated
by Dynamics Modeling with Multidimensional Tunneling," Y. Kim, A. V.
Marenich, J. Zheng, K. H. Kim, M. Kołodziejska-Huben, M. Rostkowski, P.
Paneth, and D. G. Truhlar, Journal of Chemical Theory and Computation 5, 59-67
(2009). dx.doi.org/10.1021/ct800345j
79. "Critical Role of Substrate Conformational Change in the Proton Transfer Process
Catalyzed by 4-Oxalocrotonate Tautomerase," J. Ruiz-Pernía, M. Garcia-Viloca, S.
Bhattacharyay, J. Gao D. G. Truhlar, and I. Tuñon, Journal of the American
Chemical Society 131, 2687-2698 (2009). dx.doi.org/10.101/ja8087423
80. "Direct Dynamics Study of Hydrogen-Transfer Isomerization of 1-Pentyl and 1-
Hexyl Radicals," J. Zheng and D. G. Truhlar , Journal of Physical Chemistry A 113,
11919-11925 (2009). dx.doi.org/10.1021/jp903345x
81. "Phase Space Prediction of Product Branching Ratios: Canonical Competitive
Nonstatistical Model," J. Zheng, E. Papajak, and D. G. Truhlar, Journal of the
American Chemical Society 131, 15754-15760 (2009).
x.doi.org/10.1021/ja904405v
82. "Least-Action Tunneling Transmission Coefficient for Polyatomic Reactions," R.
Meana-Pañeda, D. G. Truhlar, and A. Fernández-Ramos, Journal of Chemical
Theory and Computation 6, 6-17 (2010). dx.doi.org/10.1021/ct900420e
Polyrate 519
83. "Kinetics of Hydrogen-Transfer Isomerizations of Butoxyl Radicals," J. Zheng and D.
G. Truhlar, Physical Chemistry Chemical Physics 12, 7782-7793 (2010).
dx.doi.org/10.1039/b927504e.
84. “Free Energy Surfaces for Liquid-Phase Reactions and Their Use to Study the
Border Between Concerted and Nonconcerted -Elimination Reactions of Esters
and Thioesters,” Y. Kim, J. R. Mohrig, and D. G. Truhlar, Journal of the American
Chemical Society 131, 11071-11082 (2010). dx.doi.org/10.1021/ja101104q
85. “Computational Thermochemistry: Scale Factor Databases and Scale Factors for
Vibrational Frequencies Obtained from Electronic Model Chemistries,” I. M.
Alecu, J. Zheng, Y. Zhao, and D. G. Truhlar, Journal of Chemical Theory and
Computation 6, 2872-2887 (2010). dx.doi.org/10.1021/ct100326h.
86. “Direct Dynamics Implementation of the Least-Action Tunneling Transmission
Coefficient. Application to the CH4/CD3H/CD4+CF3 Abstraction Reactions,” R.
Meana-Pañeda, D. G. Truhlar, and A. Fernández-Ramos, Journal of Chemical
Theory and Computation 6, 3015-3025 (2010). dx.doi.org/10.1021/ct100285a
87. “Free Energy Surfaces for Liquid-Phase Reactions and Their Use to Study the
Border Between Concerted and Nonconcerted α,β-Elimination Reactions of Esters
and Thioesters,” Y. Kim, J. R. Mohrig, and D. G. Truhlar, Journal of the American
Chemical Society 132, 11071-11082 (2010). doi.org/10.1021/ja101104q
88. “High-Level Direct-Dynamics Variational Transition State Theory Calculations
Including Multidimensional Tunneling of the Thermal Rate Constants, Branching
Ratios, and Kinetic Isotope Effects of the Hydrogen Abstraction Reactions from
Methanol by Atomic Hydrogen,” R. Meana-Pañeda, D. G. Truhlar and A.
Fernández-Ramos, Journal of Chemical Physics 134, 094302/1-14 (2011).
dx.doi.org/10.1063/1.3555763
89. “Practical Methods for Including Torsional Anharmonicity in Thermochemical
Calculations of Complex Molecules: The Internal-Coordinate Multi-Structural
Approximation,” J. Zheng, T. Yu, E. Papajak, I, M. Alecu, S. L. Mielke, and D. G.
Truhlar, Physical Chemistry Chemical Physics 13, 10885-10907 (2011).
dx.doi.org/10.1039/C0CP02644A
90. “Multi-Structural Variational Transition State Theory. Kinetics of the 1,4-Hydrogen
Shift Isomerization of the Pentyl Radical with Torsional Anharmonicity,” T. Yu, J.
Zheng, and D. G. Truhlar, Chemical Science 2, 2199-2213 (2011).
dx.doi.org/10.1039/ C1SC00225B
91. “Computational Study of the Reactions of Methanol with the Hydroperoxyl and
Methyl Radicals. 2. Accurate Thermal Rate Constants,” I. M. Alecu and D. G.
Truhlar, Journal of Physical Chemistry A 115, 14599-14611 (2011).
dx.doi.org/10.1021/jp209029p
92. “Multipath Variational Transition State Theory. Rate Constant of the 1,4-Hydrogen
Shift Isomerization of the 2-Cyclohexylethyl Radical,” T. Yu, J. Zheng, and D. G.
Truhlar, Journal of Physical Chemistry A 116, 297-308 (2012).
dx.doi.org/10.1021/jp209146b
Polyrate 520
93. “Kinetics of the Hydrogen Abstraction from Carbon-3 of 1-Butanol by
Hydroperoxyl Radical: Multi-Structural Variational Transition State Calculations of
a Reaction with 262 Conformations of the Transition State,” P. Seal, E. Papajak,
and D. G. Truhlar, Journal of Physical Chemistry Letters 3, 264-271 (2012).
dx.doi.org/10.1021/jz201546e
94. “Multi-Structural Variational Transition State Theory: Kinetics of the 1,5-Hydrogen
Shift Isomerization of 1-Butoxyl Radical Including All Structures and Torsional
Anharmonicity,” X. Xu, E. Papajak, J. Zheng, and D. G. Truhlar, Physical
Chemistry Chemical Physics 14, 4204-4216 (2012).
dx.doi.org/10.1039/c2cp23692c.
95. “Multi-path Variational Transition State Theory for Chemical Reaction Rates of
Complex Polyatomic Species: Ethanol + OH Reactions,” J. Zheng and D. G.
Truhlar, Faraday Discussions 157, 59-88 (2012). dx.doi.org/10.1039/C2FD20012K.
96. “MSTor: A program for calculating partition functions, free energies, enthalpies,
entropies, and heat capacities of complex molecules including torsional
anharmonicity,” J. Zheng, S. L Mielke, K. L Clarkson, and D. G. Truhlar, Computer
Physics Communications 183, 1803-1812 (2012).
dx.doi.org/10.1016/j.cpc.2012.03.007
97. “A Product Branching Ratio Controlled by Vibrational Adiabaticity and Variational
Effects: Kinetics of the H + trans-N2H2 Reactions,” J. Zheng, R. J. Rocha, M.
Pelegrini, L. F. A. Ferrão, E. F. V. Carvalho, O. Roberto-Neto, F. B. C. Machado,
and D. G. Truhlar, Journal of Chemical Physics 136, 184310/1-10 (2012).
dx.doi.org/10.1063/1.4707734
98. "Role of Conformational Structures and Torsional Anharmonicity in Controlling
Chemical Reaction Rates and Relative Yields: Butanal + HO2 Reactions," J. Zheng,
P. Seal, and D. G. Truhlar, Chemical Science 4, 200-212 (2013).
dx.doi.org/10.1039/c2sc21090h
99. "Multi-Structural Variational Transition State Theory: Kinetics of the Hydrogen
Abstraction from Carbon-2 of 2-Methyl-1-propanol by Hydroperoxyl Radical
Including All Structures and Torsional Anharmonicity," X. Xu, T. Yu, E. Papajak,
and D. G. Truhlar, Journal of Physical Chemistry A 116, 10480-10487 (2012).
dx.doi.org/10.1021/jp307504p
100. "Biofuel Combustion. Energetics and Kinetics of Hydrogen Abstraction from
Carbon-1 in n-Butanol by the Hydroperoxyl Radical Calculated by Coupled Cluster
and Density Functional Theories and Multi-Structural Variational Transition State
Theory with Multidimensional Tunneling," I. M. Alecu, J. Zheng, E. Papajak, T.
Yu, and D. G. Truhlar, Journal of Physical Chemistry A 116, 12206-12213 (2012).
dx.doi.org/10.1021/jp308460y
101. “Kinetics of the Hydrogen Atom Abstraction Reactions from 1-Butanol by
Hydroxyl Radical: Theory Matches Experiment and Then Some,” P. Seal, G.
Oyedepo, and D. G. Truhlar, Journal of Physical Chemistry A 117, 275-282 (2013).
dx.doi.org/10.1021/jp310910f
Polyrate 521
102. “Quantum Thermochemistry: Multi-Structural Method with Torsional
Anharmonicity Based on a Coupled Torsional Potential,” J. Zheng and D. G.
Truhlar, Journal of Chemical Theory and Computation 9, 1356-1367 (2013).
dx.doi.org/10.1021/ct3010722
103. “Including Torsional Anharmonicity in Canonical and Microcanonical Reaction
Path Calculations,” J. Zheng and D. G. Truhlar, Journal of Chemical Theory and
Computation 9, 2875-2881(2013). dx.doi.org/10.1021/ct400231q
104. "MSTor version 2013: A new version of the computer code for the multistructural
torsional anharmonicity with a coupled torsional potential," J. Zheng, R. Meana-
Pañeda, and D. G. Truhlar, Computer Physics Communications 184, 2032-2033
(2013). [new version announcement] dx.doi.org/10.1016/j.cpc.2013.03.011
105. “Multi-Path Variational Transition State Theory for Chiral Molecules: The Site-
Dependent Kinetics for Abstraction of Hydrogen from Hydroperoxyl Radical,
Analysis of Hydrogen Bonding in the Transition State, and Dramatic Temperature
Dependence of the Activation Energy,” J. L. Bao, R. Meana-Pañeda, and D. G.
Truhlar, Chemical Science 6, 5866-5881 (2015). doi.org/10.1039/C5SC01848J
106. “Kinetics of Hydrogen Radical Reactions with Toluene by Chemical Activation
Theory Employing System-Specific Quantum RRK Theory Calibrated by
Variational Transition State Theory,” J. L. Bao, J. Zheng, and D. G. Truhlar,
Journal of the American Chemical Society 138, 2690-2704 (2016).
doi.org/10.1021/jacs.5b11938
107. “Silane-Initiated Nucleation in Chemically Active Plasmas: Validation of Density
Functionals, Mechanisms, and Pressure-Dependent Variational Transition State
Calculations,” J. L. Bao and D. G. Truhlar, Physical Chemistry Chemical Physics
18, 10097-10108 (2016). doi.org/10.1039/c6cp00816j
108. “Predicting Pressure-Dependent Unimolecular Rate Constants Using Variational
Transition State Theory with Multidimensional Tunneling Combined with System-
Specific Quantum RRK Theory: A Definitive Test for Fluoroform Dissociation,” J.
L. Bao, X. Zhang, and D. G. Truhlar, Physical Chemistry Chemical Physics 18,
16659-16670 (2016). doi.org/10.1039/C6CP02765B
109. “Atmospheric Chemistry of Criegee Intermediates. Unimolecular Reactions and
Reactions with Water,” B. Long, J. L. Bao, and D. G. Truhlar, Journal of the
American Chemical Society 138, 14409-14422 (2016).
doi.org/10.1021/jacs.6b08655
110. “Association of CF2 and Dissociation of C2F4 by Variational Transition State
Theory and System-Specific Quantum RRK Theory,” J. L. Bao, X. Zhang, and D.
G. Truhlar, Proceedings of the National Academy of Sciences U.S.A. 113, 13606-
13611 (2016). doi.org/10.1073/pnas.1616208113
111. “Computational Thermochemistry: Automated Generation of Scale Factors for
Vibrational Frequencies Calculated by Electronic Structure Model Chemistries," H.
S. Yu, L. J. Fiedler, I. M. Alecu, and D. G. Truhlar, Computer Physics
Communications 210, 132-138 (2017). doi.org/10.1016/j.cpc.2016.09.004
Polyrate 522
112. “Reaction of SO2 with OH in the Atmosphere,” B. Long, J. L. Bao, and D. G.
Truhlar, Physical Chemistry Chemical Physics 19, 8091-8100 (2017).
doi.org/10.1039/c7cp00497d
113. “Dual-Level Method for Estimating Multi-Structural Partition Functions with
Torsional Anharmonicity,” J. L. Bao, L. Xing, and D. G Truhlar, Journal of
Chemical Theory and Computation 13, 2511-2522 (2017).
doi.org/10.1021/acs.jctc.7b00232
114. “Variational Transition State Theory: Theoretical Framework and Recent
Developments,” J. L. Bao and D. G. Truhlar, Chemical Society Reviews 46, 7548-
7596 (2017). doi.org/10.1039/C7CS00602K
115. “Kinetics of the Methanol Reaction with OH at Interstellar, Atmospheric, and
Combustion Temperature,” L. G. Gao, J. Zheng, A. Fernández-Ramos, D. G.
Truhlar, and X. Xu, Journal of the American Chemical Society 140, 2906-2918
(2018). doi.org/10.1021/jacs.7b12773
116. “Unimolecular Reaction of Acetone Oxide and its Reaction with Water in the
Atmosphere,” B. Long, J. L. Bao, and D. G. Truhlar, Proceedings of the National
Academy of Sciences U.S.A.115, 6135-6140 (2018).
doi.org/10.1073/pnas.1804453115
117. “Hydrogen Shift Isomerizations in the Kinetics of the Second Oxidation
Mechanism of Alkane Combustion. Reactions of the Hydroperoxypentylperoxy
OOQOOH Radical,” L. Xing, J. L. Bao, X. Wang, F. Zhang, and D. G. Truhlar,
Combustion and Flame Combustion and Flame 197, 88–101 (2018).
doi.org/10.1016/j.combustflame.2018.07.013
118. “Relative Rates of Hydrogen Shift Isomerizations Depend Strongly on Multiple-
Structure Anharmonicity,” L. Xing, J. L. Bao, Z. Wang, X. Wang, and D. G.
Truhlar, Journal of the American Chemical Society 140, 17556-17570 (2018).
doi.org/10.1021/jacs.8b09381
119. “Effect of Energy Dependence of the Density of States on Pressure-Dependent Rate
Constants,” J. L. Bao and D. G. Truhlar, Physical Chemistry Chemical Physics 20,
30475-30479 (2018). doi.org/10.1039/C8CP05915B
120. “Kinetics of the Strongly Correlated CH3O + O2 Reaction: The Importance of
Quadruple Excitations in Atmospheric and Combustion Chemistry,” B. Long, J. L.
Bao, and D. G. Truhlar, Journal of the American Chemical Society 141, 611-617
(2019). doi.org/10.1021/jacs.8b11766
121. “Kinetics of the Toluene Reaction with OH Radical,” R. M. Zhang, X. Xu, and D.
G. Truhlar, Research 2019, 5373785/1-19 (2019). (Research is the first journal in
the Science Partner Journal (SPJ) program and is the official journal of the China
Association for Science and Technology (CAST).) (Open access)
doi.org/10.34133/2019/5373785
122. “Rapid Unimolecular Reaction of Stabilized Criegee Intermediates and Implications
for Atmospheric Chemistry,” B. Long, J. L. Bao, and D. G. Truhlar, Nature
Communications 10, 2003/1-8 (2019). doi.org/10.1038/s41467-019-09948-7
Polyrate 523
123. “Quantum Effects on H2 Diffusion in Zeolite RHO: Inverse Kinetic Isotope Effect
for Sieving,” L. G. Gao, R. M. Zhang, X. Xu, and D. G. Truhlar, Journal of the
American Chemical Society 134, 13635-13642 (2019).
doi.org/10.1021/jacs.9b06506
124. “Multistructural Anharmonicity Controls the Radical Generation Process in Biofuel
Combustion, L. Xing, Z. Wang, and D. G. Truhlar, Journal of the American
Chemical Society 141, 18531-18543 (2019). doi.org/10.1021/jacs.9b09194
125. “Association of Cl with C2H2 by Unified Variable-Reaction-Coordinate and
Reaction-Path Variational Transition State Theory,” L. Zhang, D. G. Truhlar,
and S. Sun, Proceedings of the National Academy of Sciences U.S.A. 117, 5610-
5616 (2020). doi.org/10.1073/pnas.1920018117
126. “Water Catalysis of the Reaction of Methanol with OH Radical in the Atmosphere
is Negligible,” J. Wu, L. G. Gao, Z. Varga, X. Xu, W. Ren, D. G Truhlar,
Angewandte Chemie International Edition 59, 10826-10830 (2020).
doi.org/10.1002/anie.202001065
127. “Large Anharmonic Effects on Tunneling and Kinetics: The Reaction of Propane
with Muonium.” L. Gao, D. G. Fleming, D. G. Truhlar, and X. Xu, Journal of
Physical Chemistry Letters 17, 4154-4159 (2021).
doi.org/10.1021/acs.jpclett.1c01229
128. “Strong dependence on multistructural anharmonicity of the relative rates of
intramolecular H-migration in alkylperoxyl and methylcyclohexylperoxyl radicals,”
L. Xing, L. Lian, and D. G. Truhlar, Combustion and Flame 231, 11503/1-12
(2021). doi.org/10.1016/j.combustflame.2021.111503
129. Atmospheric Kinetics. Bimolecular Reactions of Carbonyl Oxide by a Triple-Level
Strategy,” B. Long, Y. Wang, Y. Xia, X. He, J. L. Bao, and D. G. Truhlar, Journal
of the American Chemical Society 143, 8402-8413 (2021).
doi.org/10.1021/jacs.1c02029
22. ERRATA
All known errata to the GTST book chapter (Ref. 5 in Sect. 21) have been assembled into
a PDF file. This file is available at the Polyrate Web site.
Polyrate 524
23. ACKNOWLEDGMENTS
The authors are grateful to Da-hong Lu, Thanh N. Truong, Sachchida N. Rai, Gene C.
Hancock, Jack Lauderdale, Tomi Joseph, Michael Zhen Gu, and Steven Clayton for
contributions to early versions of POLYRATE. The development of all versions of Polyrate
was supported in part by grants from the U. S. Department of Energy, Office of Basic
Energy Sciences (principal investigator: Donald G. Truhlar, University of Minnesota).
The development of versions 6.0-6.5 of Polyrate was also supported in part by a grant
from the National Science Foundation, Department of Advanced Scientific Computing
(principal investigator: Rozeanne Steckler, San Diego Supercomputer Center).
Polyrate 525
24. INDEX
0IVTST KEYWORD DEFINITION ...................................................281
ABSORD SUBPROGRAM ......................................442
ACALC SUBPROGRAM ........................................442 ACESET SUBPROGRAM .......................................442 AITKEN SUBPROGRAM .......................................442 AITKF2 SUBPROGRAM .......................................442 AITKNF SUBPROGRAM .......................................442 ALFCT SUBPROGRAM .........................................442
ALLEXCIT KEYWORD DEFINITION ...................................................217 TESTRUN EXAMPLE ......................335, 340, 373
ANALYSIS KEYWORD DEFINITION ...................................................228
ANCOEF SUBPROGRAM ......................................442
ANGL SUBPROGRAM ..........................................442 ANGLCS SUBPROGRAM ......................................442 ANGLV SUBPROGRAM ........................................442 ANHARM SUBPROGRAM.............................. 62, 443 Anharmonicity .........................39, 40, 90, 91, 243 Anharmonicity keywords.................................163
ANHDER SUBPROGRAM .....................................443 ANTLR KEYWORD
DEFINITION ...................................................164 ARMUEF SUBPROGRAM .....................................443 ARMUEF1 SUBPROGRAM ...................................443 ARRSM SUBPROGRAM ........................................443
ARRSV SUBPROGRAM ........................................443 ASYMALP SUBPROGRAM ...................................443 ASYMCAL SUBPROGRAM ...................................443 ASYMENT SUBPROGRAM ...................................443 ASYMNZD SUBPROGRAM ...................................443 ASYMRMI SUBPROGRAM ...................................443
ATOMS KEYWORD............................... 71, 138, 299 DEFINITION ...................................................141
AVERJN SUBPROGRAM .......................................443 BANGLE1 SUBPROGRAM ....................................443 BARRI KEYWORD
DEFINITION ...................................................238
BATH KEYWORD DEFINITION ...................................................191
BCALC SUBPROGRAM ........................................444 BCALCO SUBPROGRAM ......................................444 BCALCP SUBPROGRAM ......................................444 BIMAT SUBPROGRAM .........................................444
BMAT SUBPROGRAM ..........................................444 BMAT1 SUBPROGRAM ........................................444 BMAT2 SUBPROGRAM ........................................444 BMAT5 SUBPROGRAM ........................................444 BMAT5X SUBPROGRAM .....................................444 BOLTZ SUBPROGRAM .........................................445
BOTHK KEYWORD DEFINITION ...................................................228
BRENT SUBPROGRAM ........................................ 445 BRNULI SUBPROGRAM ...................................... 445 BTEN1 SUBPROGRAM ........................................ 444
BTEN2 SUBPROGRAM ........................................ 445 BTEN5 SUBPROGRAM ........................................ 445 BTEN5X SUBPROGRAM ...................................... 445 BTENS SUBPROGRAM ........................................ 445 BTENTR SUBPROGRAM ...................................... 445 BTORSN SUBPROGRAM ...................................... 444
CALCS SUBPROGRAM ........................................ 445 CALCUB SUBPROGRAM ..................................... 445 Canonical order .................................................. 38 Canonical Variational Theory ........................... 15 CARTRP KEYWORD
DEFINITION................................................... 191
CASE SUBPROGRAM .......................................... 445 CD-SCSAG ............................................................ 48 CENTER SUBPROGRAM ................................ 62, 446 CENTR1 SUBPROGRAM ...................................... 446 CENTRAL SUBPROGRAM ................................... 446 CFLOAT SUBPROGRAM ...................................... 446
ch3tr1 test run................................................... 434 ch4cltr1 test run................................................ 426 ch4cltr2 test run................................................ 427 ch4ohtr1 test run ............................. 422, 424, 425 ch4ohtr2 test run .............................................. 423 ch4otr1 test run ................................................ 428
ch5fu29tr1 test run ........................................... 348 ch5fu29tr2 test run ........................................... 349 ch5fu30tr1 test run ........................................... 350 ch5fu30tr2 test run ........................................... 351 ch5fu30tr3 test run ........................................... 352 ch5fu30tr4 test run ........................................... 353
ch5fu30tr5 test run ........................................... 354 ch5fu30tr6 test run ........................................... 355 ch5fu31tr1 test run ........................................... 356 ch5fu40tr1 test run ........................................... 357 ch5fu40tr2 test run ........................................... 358 ch5fu40tr3 test run ........................................... 359
ch5fu40tr4 test run ........................................... 360 ch5fu40tr5 test run ........................................... 361 ch5fu40tr6 test run ........................................... 363 ch5fu50tr1 test run ........................................... 364 ch5fu50tr2 test run ........................................... 365 ch5fu50tr3 test run ........................................... 366
ch5fu51tr1 test run ........................................... 367 ch5icfu30tr1 test run ........................................ 368 ch5icfu30tr2 test run ........................................ 369 ch5icfu31tr1 test run ........................................ 370 ch5icfu40tr1 test run ........................................ 371 ch5icfu40tr2 test run ........................................ 372
ch5j1tr1 test run ............................................... 329 ch5j1tr10 test run ............................................. 340
Polyrate 526
ch5j1tr11 test run..............................................341 ch5j1tr2 test run ................................................331 ch5j1tr3 test run ................................................332 ch5j1tr4 test run ................................................333
ch5j1tr5 test run ................................................334 ch5j1tr6 test run ................................................335 ch5j1tr7 test run ................................................336 ch5j1tr8 test run ................................................337 ch5j1tr9 test run ................................................338 ch5j2itr1 test run...............................................346
ch5j2itr2 test run...............................................347 ch5j2tr1 test run ................................................342 ch5j2tr2 test run ................................................344 ch5j2tr3 test run ................................................345 CHAIN UTILITY SUBPROGRAMS ........................... 73 CHARMMRATE ..................................................... 18
CHECK KEYWORD DEFINITION ...................................................141
CHKFRE SUBPROGRAM ......................................446 CHKUP SUBPROGRAM ........................................446 CLASS SUBPROGRAM .........................................446 CLASSVIB KEYWORD
DEFINITION ...................................................141 clhbrtr1 test run.................................................373 clhbrtr2 test run.................................................375 clhbrtr3 test run.................................................376 clhbrtr4 test run.................................................377 cmctr1 test run ..................................................379
cmctr2 test run ..................................................380 cmctr3 test run ..................................................381 CMS SUBPROGRAM ............................................446 COG SUBPROGRAM ............................................446 COHBT1 SUBPROGRAM ......................................446 COHBT2 SUBPROGRAM ......................................446
COLSHF SUBPROGRAM .......................................446 comp_pot.jc ......................................................502 comp_src.jc .......................................................503 COMT .............................................................50, 52 configure ...........................................................501 CONOUT SUBPROGRAM .....................................447
CONSTANT KEYWORD DEFINITION ...................................................164
CONV40 SUBPROGRAM ......................................447 Conventional Transition State Theory .............. 15 COORD KEYWORD
DEFINITION ...................................................192
COORD UTILITY SUBPROGRAMS .......................... 72 Coordinates
Cartesian ........................................................ 43 Curvilinear ..................................................... 43 Rectilinear ...................................................... 43
CORTRM SUBPROGRAM .....................................447
COSINE SUBPROGRAM .......................................447 CROSSPROD SUBPROGRAM ................................447 CRVVEC SUBPROGRAM ......................................447 CUBIC SUBPROGRAM .........................................447
CUBIC2 SUBPROGRAM ....................................... 447 CUBST SUBPROGRAM ........................................ 447 CURV KEYWORD
DEFINITION................................................... 192
DGRAD OPTION............................................. 101 TESTRUN EXAMPLE329, 334, 338, 373, 375,
383, 384 DHESS OPTION .............................................. 101
TESTRUN EXAMPLE ................................. 336 TESTRUN EXAMPLE ................................. 333
ONESIDE OPTION .......................................... 101 TESTRUN EXAMPLE ................................. 397
CUS KEYWORD DEFINITION................................................... 228
CUSSPL SUBPROGRAM ....................................... 447 CVCOOR SUBPROGRAM ..................................... 447
CVT ...................................................................... 28 TESTRUN EXAMPLE ...................................... 334
CVT KEYWORD DEFINITION................................................... 228 TEST RUN EXAMPLE .............................329, 338 TESTRUN EXAMPLE ..............................333, 337
CVT/MEPSAG ....................................................... 50 cwmctr1 test run............................................... 382 cwmctr2 test run............................................... 383 cwmctr3 test run............................................... 384 D parameter ...................................................... 164 DATTIM SUBPROGRAM ...................................... 447
DAXPY SUBPROGRAM ....................................... 447 DDOT SUBPROGRAM .......................................... 450 DEFALT SUBPROGRAM ...................................... 447 DEFENG SUBPROGRAM ...................................... 448 DEFGEN SUBPROGRAM ...................................... 448 DEFLT40 SUBPROGRAM .................................... 448
DEFOPT SUBPROGRAM ...................................... 448 DEFPAT SUBPROGRAM ...................................... 448 DEFRAT SUBPROGRAM ...................................... 448 DEFSEC SUBPROGRAM ...................................... 448 DEFSTA SUBPROGRAM ...................................... 448 DEFTUN SUBPROGRAM ...................................... 448
DELEX1 KEYWORD DEFINITION................................................... 239
DELTA2 KEYWORD ........................................ 42, 99 DELTA2 PARAMETER ......................................... 193 DELTAE KEYWORD
DEFINITION................................................... 239
DEMIN KEYWORD DEFINITION................................................... 164
DERIV2 SUBPROGRAM ....................................... 448 DERV SUBPROGRAM .......................................... 448 DERV24 SUBPROGRAM ...................................... 448 DERVAG SUBPROGRAM ..................................... 448
DETMI KEYWORD .............................................. 491 DEFINITION................................................... 281 TESTRUN EXAMPLE ...................................... 393
detmi utility program ....................................... 491
Polyrate 527
DFGN31 SUBPROGRAM ......................................448 DGAMMA SUBPROGRAM ....................................449 DGEDI SUBPROGRAM .........................................449 DGEFA SUBPROGRAM ........................................449
DIATOM KEYWORD .............................................. 62 DEFINITION ...................................................165
DIATOM SUBPROGRAM ............................... 62, 449 DIFFD KEYWORD............................................42, 99 DIFFD PARAMETER ............................................193 DIGISTR SUBPROGRAM ......................................449
DIST SUBPROGRAM ............................................449 DL KEYWORD .....................................................102
DEFINITION ...................................................142 DLX2 KEYWORD
DEFINITION ...................................................156 DLX3 KEYWORD
DEFINITION ...................................................193 DOGLEG SUBPROGRAM ......................................449 DOPNM SUBPROGRAM .......................................449 DOREPR SUBPROGRAM ......................................449 DOREST SUBPROGRAM ......................................449 DORODS SUBPROGRAM ......................................449
DORPH SUBPROGRAM ........................................450 DOSAFR SUBPROGRAM ......................................450 DOSAGE SUBPROGRAM ......................................450 DOTPRD SUBPROGRAM ......................................450 DPMPAR SUBPROGRAM ......................................449 DPR123 SUBPROGRAM .......................................450
DPSWAP SUBPROGRAM ......................................450 DQQP KEYWORD
DEFINITION ...................................................165 RELATED KEYWORDS ...................................171
DSCAL SUBPROGRAM ........................................450 DSWAP SUBPROGRAM ........................................450
dumpot.f ........................................................71, 81 E1GEOM SECTION
DEFINITION ...................................................237 E1GRAD SECTION
DEFINITION ...................................................237 E1HESS SECTION
DEFINITION ...................................................237 EACT KEYWORD
DEFINITION ...................................................229 TESTRUN EXAMPLE .............................. 329, 338
EBND SUBPROGRAM ..........................................450 ECKARS SUBPROGRAM ......................................450
ECKART SUBPROGRAM ......................................450 ECKRT SUBPROGRAM ........................................450 EDGEOK KEYWORD
DEFINITION ...................................................229 EFFBATH SUBPROGRAM.....................................451 EFMAIN SUBPROGRAM .......................................451
EFOPT KEYWORD DEFINITION ...................................................156
EFORMD SUBPROGRAM .....................................451 EFOVLP SUBPROGRAM .......................................451
EFPHES SUBPROGRAM ....................................... 451 EHOOK SUBPROGRAM ................................. 78, 450 EIGENVECTOR KEYWORD
DEFINITION................................................... 166
ELEC KEYWORD DEFINITION................................................... 166
electronic structure input ............ 16, 63, 408, 416 Electronic structure input file
anharmonicities ............................................. 82 data interpolation .......................................... 85
Dummy potential energy surface ........... 71, 81 frequencies .................................................... 82 moment of inertia .......................................... 82 unit fu30 ................................................ 81, 241 unit fu40 ........................................................ 81 user-supplied information ............................ 83
ELLIP SUBPROGRAM .......................................... 451 ELRPH SUBPROGRAM ........................................ 451 EMIN KEYWORD
DEFINITION................................................... 217 ENDRODS SUBPROGRAM ................................... 451 ENDSLP SUBPROGRAM ...................................... 451
ENERGETICS SECTION ...............................148, 302 ENERGY KEYWORD
DEFINITION................................................... 167 ENERXN KEYWORD
DEFINITION................................................... 281 ENESAD KEYWORD
DEFINITION................................................... 281 ENORM SUBPROGRAM ....................................... 451 ENROUT SUBPROGRAM ..................................... 451 EPART SUBPROGRAM ........................................ 451 EPARTI SUBPROGRAM ....................................... 451 Equilibrium constant.......................................... 51
ERF SUBPROGRAM ............................................. 451 ES1 KEYWORD
DIFFD PARAMETER TESTRUN EXAMPLE ................................. 337
ES1 KEYWORD DELTA2 PARAMETER
TESTRUN EXAMPLE ................................. 337 METHOD DESCRIPTION ................................... 99 METHOD DESCRIPTION ................................... 42 TESTRUN EXAMPLE ...................................... 337
ES1 KEYWORD TESTRUN EXAMPLE ...................................... 342
ES1 KEYWORD TESTRUN EXAMPLE ...................................... 398
ES1OPT KEYWORD DEFINITION................................................... 193
ESD KEYWORD .............................................. 62, 99 TESTRUN EXAMPLE ..................... 333, 345, 391
Euler stabilization method................................. 42 Euler steepest-descents (ESD)method.............. 41 EVIB SUBPROGRAM ........................................... 452 EWKB SUBPROGRAM ......................................... 452
Polyrate 528
EXCITED KEYWORD DEFINITION ...................................................217
EXFIRST KEYWORD.............................................. 89 DEFINITION ...................................................193
TESTRUN EXAMPLE .............................. 385, 396 Expert users ............................................. 321, 322 EXPND SUBPROGRAM ........................................452 EXSECOND KEYWORD ......................................... 89
DEFINITION ...................................................195 TESTRUN EXAMPLE .......................................385
EXTRAP SUBPROGRAM ......................................452 EXTRP SUBPROGRAM .........................................452 EXTRP40 SUBPROGRAM .....................................452 EZERO KEYWORD................................................. 69
CALCULATE OPTION TESTRUN EXAMPLE ......................... 373, 396
DEFINITION ...................................................149 READ OPTION
TESTRUN EXAMPLE ..................................375 EZUNIT KEYWORD
DEFINITION ...................................................149 F1DI SUBPROGRAM ............................................452
F1DIM SUBPROGRAM .........................................452 FACORD SUBPROGRAM ......................................452 FCINPT SUBPROGRAM ........................................452 FCMEP SUBPROGRAM ........................................452 FCN SUBPROGRAM .............................................452 FCRATE SUBPROGRAM .......................................452
FCSCALE KEYWORD DEFINITION ...................................................195
FCSCL SUBPROGRAM .........................................452 FDIAG SUBPROGRAM .........................................453 FDIAG2 SUBPROGRAM .......................................453 FDJAC1 SUBPROGRAM .......................................453
FICLSE SUBPROGRAM ........................................453 File fu30 input
lopt options ..................................................241 File usage ..........................................................505 findb utility program ........................................497
testrun example............................................380
FINDL SUBPROGRAM..........................................453 findl utility program .........................................497
testrun example............................................380 FINDLV SUBPROGRAM .......................................453 FINOUT SUBPROGRAM .......................... 51, 64, 453 FIOPEN SUBPROGRAM ........................................453
FIRSTSTEP KEYWORD ........................................100 CUBIC OPTION
TESTRUN EXAMPLE .................396, 398, 401 DEFINITION ...................................................196 RELATED KEYWORD .....................................193
FITMAX SUBPROGRAM .......................................453
FITMX SUBPROGRAM .........................................453 FIVFT SUBPROGRAM ..........................................454 FIVPT SUBPROGRAM ..........................................454 FORMA SUBPROGRAM .......................................454
FORMBT SUBPROGRAM ..................................... 454 FORMF SUBPROGRAM........................................ 454 FORMF2 SUBPROGRAM ..................................... 454 FORMG SUBPROGRAM ....................................... 454
FORWARDK KEYWORD DEFINITION................................................... 229 TESTRUN EXAMPLE ..............................385, 386
FPRINT KEYWORD DEFINITION................................................... 152
FREQ KEYWORD
DEFINITION................................................... 167 FREQIMAG KEYWORD
DEFINITION................................................... 283 FREQMAT KEYWORD ......................................... 103
DEFINITION................................................... 282 TESTRUN EXAMPLE ..............................380, 393
FREQSCALE KEYWORD DEFINITION................................................... 197
FREQUNIT KEYWORD DEFINITION................................................... 167
FRPRMN SUBPROGRAM ..................................... 454 FRSORT SUBPROGRAM ...................................... 454
GAMESSPLUSRATE .............................................. 18 GAUSQD SUBPROGRAM ..................................... 454 GAUSSQ SUBPROGRAM ..................................... 454 GAUSSRATE ......................................................... 18 GBSLVE SUBPROGRAM ...................................... 454 GBTQL2 SUBPROGRAM ...................................... 454
GCOMP KEYWORD DEFINITION ................................................... 156
GEMM SUBPROGRAM ........................................ 455 GENERAL SECTION ....................................138, 298 Generalized transition state theory ................... 28
Canonical variational theory (CVT)........ 28, 31
Microcanonical variational theory (µVT) ..... 28 GENSEC40 SUBPROGRAM .................................. 455 GEOM KEYWORD ................................................. 69
DEFINITION................................................... 167 Geometry optimization keywords
Polyrate ....................................................... 155
GETFRQ SUBPROGRAM ...................................... 455 GFDIAG SUBPROGRAM ...................................... 455 GHOOK SUBPROGRAM ................................. 78, 455 GIVTST SUBPROGRAM ....................................... 455 GRAD SUBPROGRAM ......................................... 455 GRADDR SUBPROGRAM ..................................... 455
GSETA SUBPROGRAM ........................................ 455 GSETM SUBPROGRAM ........................................ 455 GSETP SUBPROGRAM ......................................... 455 GSPEC KEYWORD
DEFINITION................................................... 229 TESTRUN EXAMPLE ...................................... 400
GTEMP KEYWORD DEFINITION................................................... 229 TESTRUN EXAMPLE ...................................... 397
GTLOG KEYWORD
Polyrate 529
DEFINITION ...................................................230 GTST Book Chapter .......................................... 26 h2nitr1 test run..................................................421 h3o2fu31tr1 test run ............... 435, 436, 437, 438
h3tr1 test run .....................................................385 h3tr2 test run .....................................................386 h3tr3 test run .....................................................387 h3tr4 test run .....................................................388 HARMONIC KEYWORD
DEFINITION ...................................................168
HBT SUBPROGRAM .............................................456 HEADR SUBPROGRAM ........................................456 HESS KEYWORD
DEFINITION ...................................................197 HESSCAL KEYWORD
DEFINITION ...................................................152
HESSIAN KEYWORD DEFINITION ...................................................168
HHOOK SUBPROGRAM ................................ 78, 456 HINDERED ROTOR .92, 96, 97, 172, 173, 176, 282,
285, 383, 384, 425, 456, 493 HINDRT SUBPROGRAM .......................................456
HINDRT1 SUBPROGRAM .....................................456 hnitr1 test run ....................................................420 ho2tr1 test run ...................................................389 ho2tr2 test run ...................................................390 ho2tr3 test run ...................................................391 ho2tr4 test run ...................................................392
ho2tr5 test run ...................................................393 HQSC SUBPROGRAM ..........................................456 HREC KEYWORD
DEFINITION ...................................................157 HRMI KEYWORD.................................................493
DEFINITION ...................................................282
hrotor utility program .......................................493 HRPART SUBPROGRAM ......................................456 HRSET SUBPROGRAM .........................................456 HVAL SUBPROGRAM ..........................................456 HYBRD SUBPROGRAM ........................................456 HYBRD1 SUBPROGRAM ......................................456
ICFDIAG SUBPROGRAM ......................................456 ICFDRP SUBPROGRAM ........................................456 ICINT SUBPROGRAM ..........................................457 ICL KEYWORD ....................................................103 ICODAL SUBPROGRAM .......................................457 ICOPOT KEYWORD .............................................102
ICOUTRP SUBPROGRAM .....................................457 ICR KEYWORD....................................................103 ICSAVE SUBPROGRAM .......................................457 ICSVRP SUBPROGRAM ........................................457 ICVT
TESTRUN EXAMPLE ......................333, 334, 345
ICVT KEYWORD TEST RUN EXAMPLE ............................. 329, 338
IDAMAX SUBPROGRAM ......................................457 IDIRECT KEYWORD
DEFINITION................................................... 198 ILCT ................................................................... 58 IMODULE FILES
AAMOD.F90 .................................................. 488
IMOM40 SUBPROGRAM ..................................... 457 INCLUDE FILES .................................................. 441
PARAM.INC ................................................... 505 INERTA SUBPROGRAM ....................................... 458 INH KEYWORD ..................................................... 62
DEFINITION................................................... 198
TESTRUN EXAMPLE ..............................337, 385 INI KEYWORD
DEFINITION................................................... 198 INITGEO KEYWORD
DEFINITION................................................... 168 INITZE SUBPROGRAM ........................................ 458
INPUNIT KEYWORD DEFINITION................................................... 144
Input file fu29 ....................................................... 236 file fu30 ................................................. 81, 241 file fu31 ....................................................... 251
file fu40 ....................................................... 261 file fu5 ......................................................... 135
section descriptions........................137, 298 file fu50 ....................................................... 279 file fu51 ....................................................... 291
INTAB SUBPROGRAM ......................................... 458
INTABS SUBPROGRAM ....................................... 458 INTCOR SUBPROGRAM ...................................... 457 INTDEF KEYWORD
DEFINITION................................................... 198 INTEGR SUBPROGRAM ....................................... 458 INTERPOLATED OPTIMIZED CORRECTIONS
(VTST-IOC)......................................... 56, 102 INTERPOLATED VTST ...................................... 52 INTERSC SUBPROGRAM ..................................... 457 INTEUL SUBPROGRAM ....................................... 458 INTF31 SUBPROGRAM ....................................... 457 INTFNC SUBPROGRAM ....................................... 458
INTMU KEYWORD DEFINITION................................................... 199
INTPM SUBPROGRAM ........................................ 458 INTPM2 SUBPROGRAM ...................................... 458 INTRPL SUBPROGRAM ....................................... 458 INTRVL SUBPROGRAM ....................................... 457
INVRT1 SUBPROGRAM ....................................... 457 INVRT2 SUBPROGRAM ....................................... 457 INVRT3 SUBPROGRAM ....................................... 458 IOCOPT KEYWORD
DEFINITION................................................... 143 TESTRUN EXAMPLE ...................................... 380
ZERO OPTION TESTRUN EXAMPLE ................ 422, 424, 425
IRCX SUBPROGRAM ........................................... 459 IRFTG0 SUBPROGRAM ....................................... 459
Polyrate 530
IRPH SUBPROGRAM ............................................459 IRPHZ SUBPROGRAM ..........................................459 Isoinertial coordinates ..................................38, 62 ISWAP SUBPROGRAM .........................................459
ISWP KEYWORD DEFINITION ...................................................199
ISWR KEYWORD DEFINITION ...................................................199
IVTMA SUBPROGRAM ........................................459 IVTMD SUBPROGRAM ........................................459
IVTMH SUBPROGRAM ........................................459 IVTST SECTION
DEFINITION ...................................................238 IVTST0 KEYWORD................................................ 53
DEFINITION ...................................................144 IVTST0 SUBPROGRAM ........................................459
IVTST0FREQ KEYWORD DEFINITION ...................................................202
IVTST0FREQ KEYWORD INCOMPATABILITY................................202
IVTST1 KEYWORD................................................ 53 DEFINITION ...................................................144
IVTST-M ............................................................... 54 IVTST-M ..........................................................109 IVTSTMOPT KEYWORD
DEFINITION ...................................................200 JACSCF SUBPROGRAM .......................................459 JAGUARATE.......................................................... 18
KAPA SUBPROGRAM ..........................................459 KAPPAS SUBPROGRAM .......................................459 KAPVA SUBPROGRAM ................................. 64, 459 KG1 SUBPROGRAM ............................................460 Large-curvature Tunneling ..........................15, 35 LCG3 ..............................................................35, 48
LCG3 SUBPROGRAM ...........................................460 LCG4 ..............................................................35, 48 LCGIT SUBPROGRAM..........................................460 LCGSRT SUBPROGRAM .......................................460 LCGTH SUBPROGRAM ........................................460 LCNORM SUBPROGRAM .....................................460
LCNWTN SUBPROGRAM .....................................460 LCPATH SUBPROGRAM ......................................460 LCPROB SUBPROGRAM ......................................460 LCPROJ SUBPROGRAM .......................................461 LCSET SUBPROGRAM .........................................461 LCSINT SUBPROGRAM ........................................461
LCSTX SUBPROGRAM .........................................461 LCT3 KEYWORD
DEFINITION ...................................................217 LCT4...................................................................116 LCT4 KEYWORD
DEFINITION ...................................................217
LCTCOR KEYWORD DEFINITION ...................................................283
LCTDETAIL KEYWORD DEFINITION ...................................................218
OUTPUT DETAILS .......................................... 309 LCTOPT KEYWORD
DEFINITION................................................... 218 INTERPOLATE OPTION
TESTRUN EXAMPLE ................................. 375 TESTRUN EXAMPLE .....329, 334, 335, 338, 340
LCTP SUBPROGRAM ........................................... 461 LCVCOR SUBPROGRAM ..................................... 461 LCVIB SUBPROGRAM ......................................... 461 LCVMOD SUBPROGRAM .................................... 461
LCXINT SUBPROGRAM ....................................... 461 LCXTAU SUBPROGRAM ..................................... 461 LCZCRT SUBPROGRAM ...................................... 462 LIN SUBPROGRAM ............................................. 462 LIN2 SUBPROGRAM ........................................... 462 LINAXIS KEYWORD
DEFINITION................................................... 169 LININT SUBPROGRAM ........................................ 462 link_exe.jc ........................................................ 504 LINMN SUBPROGRAM ........................................ 462 LINMR SUBPROGRAM ........................................ 462 LOCATE SUBPROGRAM ...................................... 462
LOCS SUBPROGRAM .......................................... 462 LOPT OPTIONS ................................................... 241 LOPT40 SUBPROGRAM ...................................... 462 LOWFREQ KEYWORD
DEFINITION................................................... 283 LSAME SUBPROGRAM ........................................ 462
LUBKSB SUBPROGRAM ...................................... 462 LUDCMP SUBPROGRAM ..................................... 462 MAIN SUBPROGRAM .......................................... 462 Manuals .............................................................. 25 MATINV SUBPROGRAM...................................... 463 MATX SUBPROGRAM ......................................... 463
MC-TINKERATE ................................................... 18 MDMOVIE KEYWORD
DEFINITION................................................... 144 MEPINV SUBPROGRAM ...................................... 463 MEPOUT SUBPROGRAM ..................................... 463 MEPSAG ......................................................... 35, 48
MEPSRT SUBPROGRAM ...................................... 463 MEPTYPEP KEYWORD........................................ 102
DEFINITION................................................... 284 TESTRUN EXAMPLE ..............................380, 393
MEPTYPER KEYWORD ....................................... 102 DEFINITION................................................... 284
TESTRUN EXAMPLE ..............................380, 393 MF DIVIDING SURFACE.............................125, 131 microcanonical optimized multidimensional
tunneling ........................................................ 15 MICROCANONICAL Variational Theory ............ 15 MINIMUM ENERGY PATH (MEP)
CALCULATING ................................................ 41 MIRP KEYWORD
DEFINITION................................................... 285 MITS KEYWORD
Polyrate 531
DEFINITION ...................................................285 MNBRAK SUBPROGRAM .....................................463 MODULE FILES..................................................488
ALLOC.F90 ....................................................488
MOPAC program .................................................. 18 MOPEG SUBPROGRAM ........................................463 MOPHES SUBPROGRAM ......................................463 MOPOPT SUBPROGRAM ......................................463 MOPSET SUBPROGRAM ......................................463 MORATE ............................................................... 18
MORMODEL KEYWORD ........................................ 90 DEFINITION ...................................................169 MORSEI OPTION
TEST RUN EXAMPLE ....... 429, 430, 431, 432 TESTRUN EXAMPLE ........ 389, 390, 392, 397
MORSEIIIA OPTION
TEST RUN EXAMPLE .................................385 RELATED KEYWORDS .......................... 169, 170
MORSE KEYWORD ................................................ 90 DEFINITION ...................................................169 RELATED KEYWORDS ...................................169 TESTRUN EXAMPLE .... 385, 389, 390, 392, 429,
430, 431, 432 MORSEQQ KEYWORD ........................................... 90
DEFINITION ...................................................170 RELATED KEYWORDS .......................... 164, 169 TESTRUN EXAMPLE .......................................397
MUCDSC SUBPROGRAM .....................................463
MULTILEVELRATE ............................................... 18 MUSC SUBPROGRAM ..........................................464 MUSCCD SUBPROGRAM .....................................464 MUVT KEYWORD
DEFINITION ...................................................230 MUVTOPT KEYWORD
DEFINITION ...................................................231 TESTRUN EXAMPLE .............................. 389, 390
MXLNEQ SUBPROGRAM .....................................464 NATOMS VARIABLE ............................................. 70 NEARW SUBPROGRAM .......................................464 NEWT SUBPROGRAM ................................... 62, 464
NEXTPT KEYWORD DEFINITION ...................................................203
NEXTPT SUBPROGRAM .......................................464 nh3tr1 test run ...................................................394 nh3tr2 test run ...................................................395 NITER KEYWORD
DEFINITION ...................................................157 NOALLEXCIT KEYWORD
TESTRUN EXAMPLE .......................................386 NOCVT KEYWORD
TESTRUN EXAMPLE .......................................382 NONLINEAR KEYWORD
TESTRUN EXAMPLE .............................. 385, 429 NOOPT KEYWORD
TESTRUN EXAMPLE......................389, 390, 391 NOPROJECT KEYWORD
TESTRUN EXAMPLE ...................................... 398 NORMOD SUBPROGRAM ........................62, 63, 464 NOROUT SUBPROGRAM ..................................... 464 NOSADDLE KEYWORD ......................................... 44
NOST31 SUBPROGRAM ...................................... 464 NQE PARAMETER ............................................... 222 NQTH ................................................................... 49 NQTH PARAMETER ............................................ 222 NSEG2 .................................................................. 49 NSEGBOLTZ KEYWORD
TESTRUN EXAMPLE ...................................... 385 NSEGHETA KEYWORD
TESTRUN EXAMPLE ...................................... 385 NSTATE SUBPROGRAM ...................................... 464 NSTEPS KEYWORD
DEFINITION................................................... 204
NUMFRQ SUBPROGRAM ..................................... 464 NUMSTEP KEYWORD ........................................... 99
DEFINITION................................................... 152 RELATED KEYWORDS................................... 153
NUMTYP KEYWORD............................................. 98 DEFINITION................................................... 153
NWCHEMRATE..................................................... 18 OBTSRT SUBPROGRAM ...................................... 464 oh3fu30tr1 testrun............................................ 406 oh3fu30tr2 testrun............................................ 407 oh3fu30tr3 testrun............................................ 408 oh3fu30tr4 testrun............................................ 409
oh3fu30tr5 testrun............................................ 410 oh3fu30tr6 test run........................................... 411 oh3fu31tr1 test run........................................... 412 oh3fu31tr2 test run........................................... 413 oh3fu40tr1 testrun............................................ 414 oh3fu40tr2 testrun............................................ 415
oh3fu40tr3 testrun............................................ 416 oh3fu40tr4 testrun............................................ 417 oh3fu40tr5 testrun............................................ 418 oh3fu40tr6 test run........................................... 419 oh3tr1 testrun ................................................... 396 oh3tr10 testrun ................................................. 405
oh3tr2 testrun ................................................... 397 oh3tr3 test run .................................................... 92 oh3tr3 testrun ................................................... 398 oh3tr4 testrun ................................................... 399 oh3tr5 testrun ................................................... 400 oh3tr6 testrun ................................................... 401
oh3tr7 testrun ................................................... 402 oh3tr8 testrun ................................................... 403 oh3tr9 test run .................................................. 404 ohcltr1 test run ................................................. 429 ohcltr2 test run ................................................. 430 ohcltr3 test run ................................................. 431
ohcltr4 test run ................................................. 432 ohcltr5 test run ................................................. 433 OHOOK SUBPROGRAM ................................. 79, 464 OPENFI SUBPROGRAM ....................................... 464
Polyrate 532
OPT50 SUBPROGRAM .........................................465 OPT50C SUBPROGRAM .......................................465 OPTIMIZATION SECTION ........................... 154, 303 OPTION SUBPROGRAM ................................ 59, 465
OPTMIN KEYWORD OPTIMIZATION
DEFINITION ..............................................158 OPTTS KEYWORD
OPTIMIZATION DEFINITION ..............................................159
ORD31 SUBPROGRAM ........................................465 Orientation .......................................................... 84 Output
files fu41-fu47 .............................................309 OUTUNIT KEYWORD
DEFINITION ...................................................144
OVRLP SUBPROGRAM ........................................465 P1FREQ SECTION
DEFINITION ...................................................240 P1HESS SECTION
DEFINITION ...................................................237 P2FREQ SECTION
DEFINITION ...................................................240 P2HESS SECTION
DEFINITION ...................................................237 PAGEM KEYWORD..............................................100
TESTRUN EXAMPLE ..... 329, 336, 338, 385, 399 Partition function
electronic........................................................ 34 rotational ..................................................29, 34 vibrational ......................................... 29, 34, 48
PATH SECTION........................................... 181, 307 EXTRAPOLATION KEYWORDS.......................188 INTEGRATOR KEYWORDS .............................186
NES KEYWORDS ...........................................190 PRINT KEYWORDS .........................................189 SSTOR KEYWORDS ........................................190 STEP SIZE KEYWORDS ...................................186 SVRC KEYWORDS..........................................187
PATH SUBPROGRAM ...........................................465
PCFREQA KEYWORD DEFINITION ...................................................286
PCFREQS KEYWORD DEFINITION ...................................................286
PCINFO KEYWORD DEFINITION ...................................................287
PHASE KEYWORD SOLID OPTION
TESTRUN EXAMPLE ......................... 420, 421 PHID SUBPROGRAM ............................................465 PHSINT SUBPROGRAM ........................................465 PIVOT KEYWORD
DEFINITION ...................................................306 PMOI SUBPROGRAM ...........................................465 POLINT SUBPROGRAM .......................................465 POLYAT SUBPROGRAM ............................... 62, 466
POLYRATE DESCRIPTION OF SUBPROGRAMS ................. 441 DIRECTORY STRUCTURE .............................. 310 HIDDEN FILE ................................................. 501
INSTALLATION PROCEDURES ....................... 310 INSTRUCTIONS FOR GENERAL USE ............... 318 MODULE FILES.............................................. 488 PROGRAM STRUCTURE ................................... 59 RUNNING TEST RUNS.................................... 317 TESTING PROCEDURES ................................. 316
potcomp.jc ........................................................ 502 Potential energy surface ............................ 16, 441 POTENTIAL KEYWORD ........................................ 81
DEFINITION...........................................150, 302 UNIT30 OPTION
TESTRUN EXAMPLE406, 407, 408, 409, 410,
414, 415 UNIT40 OPTION
TESTRUN EXAMPLE ................ 416, 417, 418 POTINF KEYWORD ............................................... 71
DEFINITION................................................... 204 PRCORD SUBPROGRAM ..................................... 466
PRDELG KEYWORD DEFINITION................................................... 232
PRDISTMX KEYWORD DEFINITION................................................... 204
PREGPT SUBPROGRAM ...................................... 466 PREP SUBPROGRAM ..................................... 77, 466
PREPJ SUBPROGRAM .................................... 77, 466 PRINT KEYWORD
DEFINITION...........................................159, 239 PRINTSTEP KEYWORD
DEFINITION................................................... 204 PRMEP SUBPROGRAM ........................................ 466
PRMODE KEYWORD DEFINITION................................................... 170
PRNTBT SUBPROGRAM ...................................... 466 PRNTFC SUBPROGRAM ...................................... 466 PROD1 SECTION ................................................. 161 PROD2 SECTION ................................................. 161
PRODFREQ KEYWORD ....................................... 103 DEFINITION................................................... 287
Product force constant matrix .................................... 39 geometry optimization .................................. 37 zero point energy .......................................... 40
PROGRAM FILES ACESPOLY .................................................... 488 EF 489 ENERGETICS ................................................. 489 FROMBLAS.................................................... 489 GIVTST .......................................................... 489
HEADR .......................................................... 489 HOOKS .......................................................... 489 INTBSV1........................................................ 489 INTBSV2........................................................ 489
Polyrate 533
INTBSV3 ........................................................489 INTERFACE ....................................................489 IVTSTM ..........................................................490 MAIN .............................................................490
MAIN_VRCMPI ..............................................490 MOPOLY ........................................................490 POLY31 .........................................................490 POLY40 .........................................................490 POLYAG.........................................................490 POLYHL .........................................................490
POLYMQ ........................................................490 POLYRR .........................................................490 POLYSZ..........................................................490 RTPJAC ..........................................................490 VRCTST_MPI .................................................491
PROGRAM SUBPROGRAMS
SETUP ............................................................488 SURF ..............................................................488
PROJCT SUBPROGRAM ................................ 63, 466 PROJECT KEYWORD
DEFINITION ...................................................170 TESTRUN EXAMPLE .......................................386
PROJF SUBPROGRAM ..........................................466 PROJTI SUBPROGRAM ........................................466 PRPART KEYWORD
DEFINITION ...................................................232 PRPATH KEYWORD
DEFINITION ...................................................204
PRSAVEMODE KEYWORD DEFINITION ...................................................205
PRSAVERP KEYWORD .......................................... 71 DEFINITION ...................................................205
PRSQ SUBPROGRAM ...........................................466 PRVIB KEYWORD
DEFINITION ...................................................232 PSAG SUBPROGRAM ...........................................466 PSATP SUBPROGRAM .........................................467 PSATP2 SUBPROGRAM .......................................467 PSATX SUBPROGRAM .........................................467 PSATX2 SUBPROGRAM .......................................467
PTORS SUBPROGRAM .........................................467 PTQVIB SUBPROGRAM .......................................467 PTSEC40 SUBPROGRAM .....................................467 PYC1 SUBPROGRAM ...........................................467 PYC1P SUBPROGRAM .........................................467 PYC2 SUBPROGRAM ...........................................467
PYC2P SUBPROGRAM .........................................467 PYCOEF SUBPROGRAM .......................................468 QFORM SUBPROGRAM .......................................468 QQPOT SUBPROGRAM ........................................468 QQSEMI KEYWORD ........................................90, 91
DEFINITION ...................................................171
RELATED KEYWORDS ...................................165 TESTRUN EXAMPLE .............................. 345, 385
QQWKB KEYWORD.........................................90, 91 DEFINITION ...................................................171
RELATED KEYWORDS................................... 165 TESTRUN EXAMPLE ...................................... 391
QRFAC SUBPROGRAM ........................................ 468 QRSENE SUBPROGRAM ...................................... 468
QRST KEYWORD DEFINITION ................................. 221
QSLVE SUBPROGRAM ........................................ 468 QTQVIB SUBPROGRAM ...................................... 468 QUAD KEYWORD
DEFINITION................................................... 222
QUADFT SUBPROGRAM ..................................... 468 QUADR SUBPROGRAM ....................................... 468 QUADTW SUBPROGRAM .................................... 468 R1FREQ SECTION
DEFINITION................................................... 240 R1HESS SECTION
DEFINITION................................................... 237 R1MPYQ SUBPROGRAM ..................................... 469 R1UPDT SUBPROGRAM ...................................... 469 R2FREQ SECTION
DEFINITION................................................... 240 R2HESS SECTION
DEFINITION................................................... 237 RACES SUBPROGRAM ........................................ 469 RALL31 SUBPROGRAM ...................................... 469 RAN1 SUBPROGRAM .......................................... 469 RANALY SUBPROGRAM ..................................... 469 RANGEIC KEYWORD
DEFINITION................................................... 289 RATE SECTION ...........................................224, 308 Rate section
print keywords............................................. 227 RATE SUBPROGRAM ..............................51, 64, 469 RATOMS SUBPROGRAM ..................................... 469
RBASIS SUBPROGRAM ....................................... 468 RBATH SUBPROGRAM ........................................ 468 RCFREQA KEYWORD
DEFINITION................................................... 288 RCFREQS KEYWORD
DEFINITION................................................... 288
RCINFO KEYWORD DEFINITION................................................... 289
RCNST SUBPROGRAM ........................................ 469 RD40EXTR SUBPROGRAM ................................. 469 RD40GEN SUBPROGRAM ................................... 469 RD40RP SUBPROGRAM ...................................... 469
RDETIL SUBPROGRAM ....................................... 469 RDHESS SUBPROGRAM ...................................... 470 RDIATM SUBPROGRAM ...................................... 469 RDIFFU SUBPROGRAM ....................................... 470 RDLN SUBPROGRAM .......................................... 470 REACFREQ KEYWORD
DEFINITION................................................... 290 REACT SUBPROGRAM .................................. 62, 470 REACT1 SECTION............................................... 161 REACT2 SECTION............................................... 161
Polyrate 534
Reactant force constant matrix..................................... 39 geometry optimization .................................. 37 properties ....................................................... 37
zero point energy ........................................... 40 REACTCOM SUBPROGRAM .................................470 Reaction coordinate......................................29, 40
determining the sign of ................................. 65 Reaction path ................................... 29, 40, 41, 50
Euler stabilization method ............................ 42
negative generalized normal mode eigenvalue ................................................................... 50
projected force constant matrix .................... 43 save grid ...................................................43, 63 step sizes ......................................................100
Reaction rate methods keywords.....................226
Reaction rates ..................................................... 48 generalized free energy of activation ........... 48 transmission coefficients............................... 48 transmission probabilities ............................. 48
Boltzmann average ................................... 47 READ5 SUBPROGRAM ................................. 59, 470
READIC SUBPROGRAM .......................................470 READINT SUBPROGRAM .....................................470 READLN SUBPROGRAM ......................................470 REARG1 SUBPROGRAM ......................................470 RECS31 SUBPROGRAM .......................................470 REDGEO SUBPROGRAM ............................... 59, 470
REDMU SUBPROGRAM .......................................471 References
bibliography .................................................512 convention explained ..............................26, 27 footnotes to text ...........................................508
REFOPT SUBPROGRAM .......................................471
RELEC SUBPROGRAM .........................................471 RENERG SUBPROGRAM ......................................471 REORDER KEYWORD
DEFINITION ...................................................205 REPFL SUBPROGRAM ................................ 471, 475 RES1 SUBPROGRAM ...........................................471
RESTART KEYWORD ................................... 66, 106 DEFINITION ...................................................145 TESTRUN EXAMPLE ..... 329, 331, 334, 383, 384
RESTOR SUBPROGRAM ................................ 59, 471 RESTRT SUBPROGRAM .......................................471 RETRY KEYWORD
DEFINITION ...................................................159 Reverse rate constant........................... 31, 50, 103 REVKEXP KEYWORD
DEFINITION ...................................................232 TESTRUN EXAMPLE ......................389, 390, 391
REXTRP SUBPROGRAM .......................................471
REZERO SUBPROGRAM ......................................471 REZERU SUBPROGRAM ......................................471 RFCFAC SUBPROGRAM .......................................471 RFREQ SUBPROGRAM .........................................471
RGEM31 SUBPROGRAM ..................................... 471 RGEN SUBPROGRAM .......................................... 472 RGEN31 SUBPROGRAM ...................................... 472 RGENER SUBPROGRAM...................................... 472
RGEOM SUBPROGRAM ....................................... 472 RGRD SUBPROGRAM .......................................... 472 RGRD31 SUBPROGRAM ..................................... 472 RGSAD SUBPROGRAM........................................ 472 RGSPEC SUBPROGRAM ...................................... 472 RGSZM SUBPROGRAM ....................................... 472
RGTEMP SUBPROGRAM ..................................... 472 RGZMAT SUBPROGRAM ..................................... 472 RHES31 SUBPROGRAM ...................................... 472 RHESS SUBPROGRAM ........................................ 472 RHESSC SUBPROGRAM ...................................... 473 RHFSEC SUBPROGRAM ...................................... 473
RHSS31 SUBPROGRAM ...................................... 473 RICOPT SUBPROGRAM ....................................... 473 RLCT SUBPROGRAM .......................................... 473 RLINE SUBPROGRAM ......................................... 473 RLOWFR SUBPROGRAM ..................................... 473 RMUVT SUBPROGRAM ....................................... 473
RODS KEYWORD DEFINITION................................................... 205
ROPT SUBPROGRAM .......................................... 473 ROPT31 SUBPROGRAM ...................................... 473 ROPTOP SUBPROGRAM ...................................... 473 rotate utility program ....................................... 497
RPART SUBPROGRAM ........................................ 473 RPARTI SUBPROGRAM ....................................... 473 RPATH SUBPROGRAM ........................................ 473 RPH31 SUBPROGRAM ........................................ 473 RPH40 SUBPROGRAM ........................................ 474 RPHAIT SUBPROGRAM ....................................... 474
RPHB SUBPROGRAM .......................................... 474 RPHDXN SUBPROGRAM ..................................... 474 RPHEXP SUBPROGRAM ...................................... 474 RPHFIT SUBPROGRAM ....................................... 474 RPHFT2 SUBPROGRAM ...................................... 474 RPHFT3 SUBPROGRAM ...................................... 474
RPHG1 SUBPROGRAM ........................................ 474 RPHG2 SUBPROGRAM ........................................ 474 RPHG5 SUBPROGRAM ........................................ 474 RPHINT SUBPROGRAM ....................................... 474 RPHMEF SUBPROGRAM ..................................... 474 RPHNWT SUBPROGRAM ..................................... 475
RPHRD1 SUBPROGRAM ...................................... 475 RPHRD2 SUBPROGRAM ...................................... 475 RPHSET SUBPROGRAM ...................................... 475 RPHTRF SUBPROGRAM ...................................... 475 RPHTRX SUBPROGRAM ...................................... 475 RPHWRT SUBPROGRAM ..................................... 475
RPIVOT SUBPROGRAM ....................................... 475 RPL KEYWORD................................................... 106 RPM KEYWORD
DEFINITION ................................................... 206
Polyrate 535
RPNT31 SUBPROGRAM .......................................475 RPOTET SUBPROGRAM .......................................475 RPOTGE SUBPROGRAM ......................................475 RPRMEP SUBPROGRAM ......................................475
RPRVIB SUBPROGRAM .......................................476 RPSEC40 SUBPROGRAM .....................................476 RP-VTST rate constants .................................... 15 RQCOM SUBPROGRAM .......................................476 RQRST SUBPROGRAM .........................................476 RQUAD SUBPROGRAM .......................................476
RRANGE SUBPROGRAM ......................................476 RRATE SUBPROGRAM ........................................476 RRPM SUBPROGRAM ..........................................476 RRSTRT SUBPROGRAM .......................................476 RSCT SUBPROGRAM ...........................................476 RSECND SUBPROGRAM ......................................476
RSFRST SUBPROGRAM .......................................476 RSP SUBPROGRAM .............................................476 RSPDRV SUBPROGRAM ......................................476 RSPECL SUBPROGRAM .......................................477 RSPP SUBPROGRAM ............................................477 RSSTOP SUBPROGRAM .......................................477
RST SUBPROGRAM .............................................477 RSTAT SUBPROGRAM .........................................477 RSTATE SUBPROGRAM .......................................477 RSVRC SUBPROGRAM ........................................477 RTEMP SUBPROGRAM ........................................477 RTITLE SUBPROGRAM ........................................477
RTOR SUBPROGRAM ..........................................477 RTOROPT SUBPROGRAM ....................................477 RTPJAC SUBPROGRAM .......................................477 RTUNNL SUBPROGRAM ......................................477 RUNM31 SUBPROGRAM .....................................477 RVAR6 SUBPROGRAM ........................................478
RVARY SUBPROGRAM ........................................478 RVPERT SUBPROGRAM .......................................478 RVRANG SUBPROGRAM .....................................478 RVRCOPT SUBPROGRAM ....................................478 RWKB SUBPROGRAM .........................................478 RWORD SUBPROGRAM .......................................478
RZVAR SUBPROGRAM ........................................478 SADDLE KEYWORD .............................................. 41
DEFINITION ...................................................206 SADDLE SUBPROGRAM ............................... 41, 478 SADENG SUBPROGRAM ......................................478 SADFREQ KEYWORD
DEFINITION ...................................................290 SADSEC40 SUBPROGRAM ..................................479 Sample test runs................................................326 Save grid .......................................................43, 63 SAVEXRP SUBPROGRAM ....................................479 SCALE KEYWORD
DEFINITION ...................................................160 SCALEMASS KEYWORD........................................ 63
DEFINITION ...................................................206 TESTRUN EXAMPLE .......................................332
SCLPT KEYWORD DEFINITION................................................... 207
Scripts comp_pot.jc ................................................. 502
comp_src.jc ................................................. 503 link_exe.jc ................................................... 504 potcomp.jc ................................................... 502
SCT KEYWORD DEFINITION................................................... 222 TESTRUN EXAMPLE ..............................329, 338
SCTOPT KEYWORD DEFINITION................................................... 223 LAGRANGE OPTION ...................................... 101
TESTRUN EXAMPLE .........................336, 342 TESTRUN EXAMPLE ................................. 332
TESTRUN EXAMPLE
SPLINE OPTION ........................................ 333 SDEB1 KEYWORD
DEFINITION ................................................... 207 SDEB2 KEYWORD
DEFINITION ................................................... 207 SDSTART KEYWORD
DEFINITION................................................... 160 SECCEN SUBPROGRAM ...................................... 479 SECCEP SUBPROGRAM ....................................... 479 Second derivatives
central differences ....................................... 101 numerical ....................................................... 98
numerical fourth order polynomial .............. 98 quadratic fit ................................................... 98
SECOND SECTION .............................................. 151 SECOND SECTION KEYWORDS
POLYRATE ..................................................... 151 SENOUT SUBPROGRAM ...................................... 479
SETANH SUBPROGRAM ...................................... 479 SETLGS SUBPROGRAM ....................................... 479 SETUP SUBPROGRAM .............................69, 74, 479 SETVAR SUBPROGRAM ...................................... 479 SEX1 KEYWORD
DEFINITION................................................... 239
SFIRST KEYWORD .............................................. 100 DEFINITION................................................... 208 TESTRUN EXAMPLE ..............................342, 396
SGND3V SUBPROGRAM ..................................... 479 SHFTSAD SUBPROGRAM .................................... 479 SIGMAF KEYWORD
DEFINITION...........................................232, 308 SIGMAR KEYWORD
DEFINITION................................................... 233 SIGN KEYWORD ................................................... 65
DEFINITION................................................... 208 SIGS SUBPROGRAM ............................................ 479
SIMPSN SUBPROGRAM ....................................... 480 SINE SUBPROGRAM ........................................... 480 Small-curvature Tunneling.......................... 15, 35 SNHCSH SUBPROGRAM ...................................... 480
Polyrate 536
SORT31 SUBPROGRAM .......................................480 SORTG SUBPROGRAM ........................................480 SPECIES KEYWORD
DEFINITION ...................................................171
SPECSTOP KEYWORD DEFINITION ...................................................209
SPL1B1 SUBPROGRAM .......................................480 SPL1B2 SUBPROGRAM .......................................480 SPL1D1 SUBPROGRAM .......................................480 SPL31 SUBPROGRAM .........................................480
SPLM31 SUBPROGRAM ......................................481 SPLNB SUBPROGRAM .........................................480 SPLNF SUBPROGRAM .........................................480 SPLNM SUBPROGRAM ........................................480 SPLNMF SUBPROGRAM ......................................481 SPLNV SUBPROGRAM .........................................481
SPLRMI SUBPROGRAM .......................................481 SPLSPV SUBPROGRAM .......................................481 SPLV31 SUBPROGRAM .......................................481 SPRNT KEYWORD
DEFINITION ...................................................210 SRANGE KEYWORD
DEFINITION ...................................................210 TESTRUN EXAMPLE ......................392, 394, 395
SSAVE SUBPROGRAM .........................................481 SSPECIAL KEYWORD
DEFINITION ...................................................210 TESTRUN EXAMPLE .......................................391
SSPECPR KEYWORD DEFINITION ...................................................211
SS-QRRK............................................... 2, 12, 500 SSTEP KEYWORD..................................... 42, 62, 99
DEFINITION ...................................................211 TESTRUN EXAMPLE ......................334, 337, 385
SSTOR ......................................... 90, 172, 190, 211 SSX SUBPROGRAM .............................................481 START SECTION..................................................161 STAT31 SUBPROGRAM .......................................481 STATE KEYWORD
ADIAB OPTION
TESTRUN EXAMPLE ..................................399 DEFINITION ...................................................233 DIAB OPTION
TESTRUN EXAMPLE ..................................400 STATEOPT KEYWORD
DEFINITION ...................................................234
STATUS KEYWORD DEFINITION ...................................................171
STAUV SUBPROGRAM ........................................481 STLGSJ SUBPROGRAM ........................................482 STOR SUBPROGRAM ...........................................482 STPTOL KEYWORD
DEFINITION ....................................................160 STVARJ SUBPROGRAM .......................................482 SUPERMOL KEYWORD
DEFINITION ...................................................145
SURF SUBPROGRAM ................. 69, 70, 72, 74, 482 SVBCMP SUBPROGRAM ..................................... 482 SVBKSB SUBPROGRAM ...................................... 482 SVRC KEYWORD
DEFINITION................................................... 307 SYMMETRY KEYWORD
DEFINITION................................................... 211 TESTRUN EXAMPLE ..............................387, 388
TABLE SUBPROGRAM ........................................ 482 TAUV SUBPROGRAM .......................................... 482
TEMP KEYWORD DEFINITION................................................... 235 RELATED KEYWORDS...........................228, 229 TESTRUN EXAMPLE ............. 329, 338, 389, 390
THETA2 SUBPROGRAM ...................................... 482 THETA3 SUBPROGRAM ...................................... 482
TITLE KEYWORD DEFINITION................................................... 146
TITLE SUBPROGRAM .......................................... 482 TOR KEYWORD
DEFINITION................................................... 172 TESTRUN EXAMPLE ..................... 383, 384, 422
TOROPT KEYWORD DEFINITION................................................... 173
TP SUBPROGRAM ............................................... 482 TPCDSC SUBPROGRAM ...................................... 483 TQL2 SUBPROGRAM .......................................... 483 TQLRAT SUBPROGRAM ...................................... 483
TRANFC SUBPROGRAM ...................................... 483 TRANG SUBPROGRAM ....................................... 483 TRANLF SUBPROGRAM ...................................... 483 TRANS SUBPROGRAM ........................................ 483 TRANS2 SUBPROGRAM ...................................... 483 TRANSF SUBPROGRAM ...................................... 483
Transmission coefficients......... 31, 35, 36, 48, 49 TRBAK3 SUBPROGRAM ..................................... 483 TRED3 SUBPROGRAM ........................................ 483 TREPT SUBPROGRAM ......................................... 483 TRLFRP SUBPROGRAM ....................................... 483 TSC SUBPROGRAM ............................................. 484
TSFREQ SECTION DEFINITION................................................... 240
TSGCOMP KEYWORD DEFINITION ................................................... 156
TSHESS SECTION DEFINITION................................................... 237
TSHREC KEYWORD DEFINITION................................................... 157
TSOUT SUBPROGRAM .................................. 51, 484 TSPSI SUBPROGRAM .......................................... 484 TSRATE SUBPROGRAM ................................ 51, 484 TST
TESTRUN EXAMPLE ...................................... 334 TST KEYWORD
DEFINITION................................................... 235 TESTRUN EXAMPLE ...................................... 382
Polyrate 537
TUNNEL SECTION ...............................................213 Tunneling
canonical optimized multidimensional ........ 52 interpolation of effective reduced mass .....101
microcanonical optimized multidimensional ................................................................... 52
TURNPT SUBPROGRAM ......................................484 UNITMI KEYWORD
DEFINITION ...................................................290 TESTRUN EXAMPLE .......................................393
UNITS KEYWORD DEFINITION ...................................................239
UPCAS SUBPROGRAM .........................................484 UPCSE SUBPROGRAM .........................................484 UPDHR SUBPROGRAM ........................................484 UPDMI SUBPROGRAM .........................................484
US KEYWORD DEFINITION ...................................................235 TESTRUN EXAMPLE .............................. 389, 390
Utility routines chain ............................................................... 73 coord............................................................... 72
VALVAG SUBPROGRAM .....................................484 VANHAR KEYWORD
DEFINITION ...................................................178 TESTRUN EXAMPLE ..... 345, 383, 384, 385, 391
VARIABLE KEYWORD .......................................... 91 Variable Reaction Coordinate and Multifaceted
Dividing Surface algorithm ............... 125, 131 VECCON SUBPROGRAM ......................................485 VECMAG SUBPROGRAM .....................................485 VIB KEYWORD
DEFINITION ...................................................179 VICLCG SUBPROGRAM .......................................485
VIVT SUBPROGRAM ...........................................485 VPART SUBPROGRAM ........................................485 VPARTI SUBPROGRAM .......................................485 VPFEXP KEYWORD
DEFINITION ...................................................235 TESTRUN EXAMPLE .............................. 332, 336
VRANGE KEYWORD ............................................. 91 DEFINITION ...................................................180
VRC ....................................................................125 VRC KEYWORD ..................................... 44, 59, 299
DEFINITION ...................................................300 VRCNEJ SUBPROGRAM .......................................485
VRCOPT KEYWORD DEFINITION ...................................................300
VRCTST SUBPROGRAM .......................................485 VSCALE KEYWORD
DEFINITION ...................................................212 VSPLI2 SUBPROGRAM ........................................485
VSPLIN SUBPROGRAM ........................................485 VTMUSN SUBPROGRAM .....................................485 VTST-IOC ......................................................... 56 VTST-ISPE .......................................................106
WELLP SECTION................................................. 161 WELLR SECTION ................................................ 161 WIGNER KEYWORD
DEFINITION................................................... 223
Wigner tunneling ......................................... 40, 48 WKB KEYWORD ....................................... 90, 91, 92
DEFINITION................................................... 180 TESTRUN EXAMPLE ...................................... 398
WKB METHOD based on true potential .................................. 92
PRIMITATIVE .................................................. 91 UNIFORM ........................................................ 91
WKBENE SUBPROGRAM ..................................... 486 WKBPOT SUBPROGRAM ..................................... 486 WKBVIB SUBPROGRAM ..................................... 486 WRITE62 KEYWORD
DEFINITION................................................... 146 WRITEFU30 KEYWORD
DEFINITION................................................... 146 WRITEFU31 KEYWORD
DEFINITION................................................... 147 WRTHOK SUBPROGRAM .................................... 486
WRTWEL SUBPROGRAM .................................... 486 WTITLE SUBPROGRAM ...................................... 485 WVAR6 SUBPROGRAM ....................................... 486 XDOTP SUBPROGRAM ........................................ 486 XERBLA SUBPROGRAM...................................... 486 XPROD SUBPROGRAM........................................ 486
YDER24 SUBPROGRAM ...................................... 486 YDERV2 SUBPROGRAM ..................................... 486 YNEWT SUBPROGRAM ....................................... 486 YSECEN SUBPROGRAM ...................................... 487 YSECEP SUBPROGRAM ...................................... 487 YTRANS SUBPROGRAM...................................... 487
ZCT KEYWORD DEFINITION................................................... 223 TESTRUN EXAMPLE ....329, 333, 334, 335, 338,
340, 422, 424, 425 Zero of energy .................................................... 68 Zero-curvature Tunneling ........................... 15, 35
ZEROPT SUBPROGRAM ...................................... 487 ZERP SUBPROGRAM ........................................... 487 ZIGAMA SUBPROGRAM...................................... 487 ZOC3P SUBPROGRAM ........................................ 487 ZOCAST SUBPROGRAM ...................................... 487 ZOCFRE SUBPROGRAM ...................................... 487
ZOCPAR SUBPROGRAM ...................................... 487 ZOCPRN SUBPROGRAM ...................................... 487 ZOCUPD SUBPROGRAM...................................... 487 ZOCVCL SUBPROGRAM...................................... 487 ZRIDDR SUBPROGRAM ...................................... 488 ZROUT SUBPROGRAM ........................................ 488
ZRPTE SUBPROGRAM ......................................... 488 ZSPMEP SUBPROGRAM ...................................... 488 µOMT ................................................................... 52 µVT ...................................................................... 28
Polyrate 538
